HelioSwarm: A Multipoint, Multiscale Mission to Characterize

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HelioSwarm: A Multipoint, Multiscale

Mission to Characterize Turbulence

Kristopher G. Klein

, Harlan Spence

, Olga

Alexandrova

, Matthew Argall

, Lev Arzamasskiy

, Jay

Bookbinder

, Theodore Broeren

, Damiano

Caprioli

, Anthony Case

, Benjamin Chandran

, Li-Jen

Chen

, Ivan Dors

, Jonathan Eastwood

, Colin

Forsyth

, Antoinette Galvin

, Vincent Genot

, Jasper

Halekas

, Michael Hesse

, Butler Hine

, Tim

Horbury

, Lan Jian

, Justin Kasper

, Matthieu

Kretzschmar

, Matthew Kunz

, Benoit Lavraud

10,15

, Olivier

Le Contel

, Alfred Mallet

, Bennett Maruca

, William

Matthaeus

, Jonathan Niehof

, Helen O’Brian

, Christopher

Owen

, Alessandro Retino

, Christopher Reynolds

, Owen

Roberts

, Alexander Schekochihin

, Ruth Skoug

, Charles

Smith

, Sonya Smith

, John Steinberg

, Michael

Stevens

, Adam Szabo

, Jason TenBarge

, Roy

Torbert

, Bernard Vasquez

, Daniel Verscharen

, Phyllis

Whittlesey

, Brittany Wickizer

, Gary Zank

and Ellen

Zweibel

Lunar and Planetary Laboratory, University of Arizona, Tucson,

AZ 85721, USA.

Space Science Center, University of New Hampshire, Durham,

NH 03824, USA.

Observatoire de Paris, LESIA, Meudon, 92190, France.

Institute for Advanced Study, Princeton, NJ, 08540, USA.

Department of Astronomy & Astrophysics, University of

Chicago Chicago, IL, 60637, USA.

BWX Technologies, Inc. Washington DC, 20001, USA.

Heliophysics Science Division, NASA Goddard Space Flight

Center, Greenbelt, MD, 20771, USA.

arXiv:2306.06537v1 [physics.plasm-ph] 10 Jun 2023

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2 HelioSwarm

Blackett Laboratory, Imperial College London London, SW7

2AZ, UK.

Mullard Space Science Laboratory, University College London

Dorking, RH5 6NT, UK.

Institut de Recherche en en Astrophysique et Planetologie,

31028 Toulouse, France.

Department of Physics and Astronomy, University of Iowa,

Iowa City, IA 52242, USA.

Ames Research Center, NASA, Mountain View, CA, 94043,

USA.

Laboratoire de Physique et Chimie de l’Environnement et de

l’Espace, CNRS and Universit´e d’Orl´eans, 45071 Orl´eans, France.

Department of Astrophysical Sciences, Princeton University

Princeton, NJ, 08540 USA.

Laboratoire d’astrophysique de Bordeaux, Univ. Bordeaux,

CNRS, Pessac, France.

Laboratoire de Physique des Plasmas, CNRS/Sorbonne

Universit´e/Universit´e Paris-Saclay/Observatoire de Paris/Ecole

Polytechnique Institut Polytechnique de Paris, Paris, 75005

France.

Space Sciences Laboratory, University of California Berkeley,

Berkeley, CA 94720, USA.

Department of Physics & Astronomy, University of Delaware,

Newark, DE 19716, USA.

Institute of Astronomy, University of Cambridge, Cambridge,

CB3 OHA, UK.

Space Research Institute, Austrian Academy of Sciences, Graz,

Austria.

Rudolf Peierls Centre for Theoretical Physics, University of

Oxford, Oxford, OX1 3PU, UK.

Los Alamos National Laboratory, Las Alamos, NM 87545, USA.

Center for Astrophysics, Harvard & Smithsonian Cambridge,

MA 02138, USA.

Department of Space Science, University of Alabama in

Huntsville Huntsville, AL 35899, USA.

Department of Astronomy, University of Wisconsin-Madison

Madison, WI 53706, USA.

*Corresponding author(s). E-mail(s): [email protected];

harlan.sp[email protected];

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HelioSwarm 3

Abstract

HelioSwarm (HS) is a NASA Medium-Class Explorer mission of the

Heliophysics Division designed to explore the dynamic three-dimensional

mechanisms controlling the physics of plasma turbulence, a ubiquitous

process occurring in the heliosphere and in plasmas throughout the uni-

verse. This will be accomplished by making simultaneous measurements

at nine spacecraft with separations spanning magnetohydrodynamic and

sub-ion spatial scales in a variety of near-Earth plasmas. In this paper, we

describe the scientiﬁc background for the HS investigation, the mission

goals and objectives, the observatory reference trajectory and instrumen-

tation implementation before the start of Phase B. Through multipoint,

multiscale measurements, HS promises to reveal how energy is trans-

ferred across scales and boundaries in plasmas throughout the universe.

Keywords: Turbulence, Space Plasma, Heliophysics, NASA Mission,

HelioSwarm

1 Introduction

Turbulence is multiscale disorder. It is the process by which energy that has

been injected into a system is transported between ﬂuctuating magnetic ﬁelds

and plasma motion with larger and smaller spatial scales. Once this cascade

of energy reaches suﬃciently small scales, dissipation mechanisms can act

eﬃciently to remove energy from the ﬂuctuations, leading to heating of the con-

stituent particles. Observations from single spacecraft provide only information

along a single path through a turbulent system; leveraging such measure-

ments to understand turbulence relies on assumptions about the underlying

spatial and temporal structure. Clusters of four spacecraft provide more infor-

mation about spatial structure, but are sensitive to only a single scale for a

given conﬁguration. Understanding fundamental processes such as turbulence

requires characterizing the underlying ﬂuctuations and their dynamic evolu-

tion across many characteristic scales simultaneously. HelioSwarm (HS) is a

Heliophysics Division NASA Medium-Class Explorer mission designed to make

such multiscale observations.

HS, currently in Phase B-prep, is the ﬁrst mission that will make the

required measurements to transform the current understanding of space

plasma turbulence, using a ﬁrst-ever swarm of nine spacecraft (SC), composed

of one Hub and eight Nodes. The nine spacecraft, comprising the HelioSwarm

Observatory, co-orbit in a lunar resonant Earth orbit, with a 2-week period,

a mean-apogee radius of ∼ 60R

and a mean-perigee radius of ∼ 11R

where R

= 6.371 × 10

m is the Earth’s radius. This orbit, illustrated in

Figure 1, enables measurements of a variety of near-Earth plasma environ-

ments, including the pristine solar wind (SW), the magnetically connected

foreshock, the magnetosheath, and the magnetosphere. Carefully designed

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4 HelioSwarm

-60

-30

-60-30 0 30 60

GSE

Solar Wind

Magnetosphere

Connected

& Foreshock

-30

-15

-60-30 0 30 60

GSE

‘

´1000

0 1000

´1000 0 1000

Hour 2478 X

GSE

(km)

GSE

(km)

The Hel ioSwarm Observatory:

Phase-B Desi g n Reference Mission

´1000 0 1000

GSE

(km)

GSE

(km)

´1000 0 1000

GSE

(km)

GSE

(km)

Observatory

Moon

Node Hub

Fig. 1: HelioSwarm Observatory Conﬁguration drawn from the Phase B

Design Reference Mission (DRM) trajectory. In the right row, the Observa-

tory location (black pentagon) and orbits relative to Earth over the 12-month

science phase are shown in both the X-Y and X-Z GSE planes. Lunar position

is indicated by an open circle for reference, with diﬀerent regions of near-

Earth plasmas indicated with color. The connected foreshock is here deﬁned

based on a typical Parker spiral orientation. The remaining panels charac-

terize two-dimensional projections of the relative conﬁgurations of the eight

Nodes (black) with respect to the central Hub (red) in Geocentric Solar Eclip-

tic (GSE) co¨ordinates. A video of the HS DRM Conﬁguration throughout the

Science Phase is available in Online Resource 1.

trajectories produce separations between the spacecraft spanning magnetohy-

drodynamic (MHD) and sub-ion (e.g., ion gyroradius) spatial scales, allowing

us to address a broad set of questions about the three-dimensional dynam-

ics of magnetized turbulence. Answering these open questions was identiﬁed

as a science priority in the 2013 Heliophysics Decadal Survey[1] and is deeply

rooted in decades-earlier recommendations by the space science community in

the 1980 report by the Plasma Turbulence Explorer Study Group[2]. As the

ﬁrst multipoint, multiscale mission, HS gives an unprecedented view into the

nature of space plasma turbulence.

In Sec. 2, we describe the scientiﬁc motivation for HS and in Sec. 3 we

enumerate the speciﬁc mission goals and objectives. Secs. 4 and 5 describe the

requirements on what the missions will measure and the observatory trajecto-

ries and instrumentation. Sec. 6 illustrates the application of analysis methods

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HelioSwarm 5

to synthetic data modeling future observations drawn from numerical simu-

lations of turbulence. Conclusions and ongoing work towards the scheduled

launch date at the end of this decade are discussed in Sec. 7.

2 Scientiﬁc Background and Motivation

Turbulent systems consist of ﬂuctuations spanning a wide range of spatial

and temporal scales. Fluctuations interact nonlinearly, typically with a net

transfer of energy from larger to smaller spatial scales. This process, the

energy cascade, couples the injection range of scales, through a lossless inertial

range, into a dissipation range where heating occurs. Turbulence in plasmas

is signiﬁcantly more complex than in hydrodynamics: plasma motion couples

to dynamically signiﬁcant electromagnetic ﬁelds, the system possesses many

characteristic spatial and temporal scales, supports many diﬀerent waves and

ﬂuctuations, and in weakly collisional systems many mechanisms other than

viscosity can act to dissipate the cascade. Additional details on the current

state of plasma turbulence research can be found in recent reviews, e.g. [3–5].

The most energetic SW ﬂuctuations are non-compressive [6] with properties

resembling Alfv´en waves [7–9]. Diﬀerent types of ﬂuctuations nonlinearly inter-

act in diﬀerent ways [8, 10–13] resulting in dramatically diﬀerent outcomes.

The ubiquity of turbulence in space and astrophysical plasmas makes it a lead-

ing candidate for the process governing the thermodynamics of a wide range of

systems. For instance, turbulence is conjectured to enable angular momentum

transport in accretion disks [14], amplify galactic magnetic ﬁelds [15], aﬀect

transport processes [16] and establish high temperatures [17] in the intraclus-

ter medium of galaxy clusters, determine the dispersal and mixing of elements

in the Interstellar Medium (ISM) [18], and play a key role in star formation

[19].

SW turbulence at the injection scales is driven by large-scale structures[20,

21]. Recent observations from Parker Solar Probe (PSP) indicate that this

regime is formed due to SW processing in the near-Sun environment [22, 23].

Measurements of the scale-to-scale rate of energy transfer, the cascade rate,

near the end of the injection range generally agree with rates near the start of

the inertial range, as has been explicitly demonstrated with Magnetospheric

Multiscale (MMS) observations [24].

Inertial-range observations [25] exhibit scale-invariant energy transfer con-

sistent with Kolmogorov theory [26, 27]: turbulent structures splitting into

ever-smaller ﬂuctuations while conserving energy. The inertial range plasma

behaves like a MHD ﬂuid [28], with MHD turbulence theory describing rele-

vant phenomena in space physics and astrophysics [29–31] and predicting some

SW features [5, 32, 33]. For example, Figure 2 shows a composite interplane-

tary magnetic ﬁeld (IMF) power spectrum from three magnetometers at 1 AU

measured over diﬀerent time intervals from tens of days to an hour as the SW

rapidly sweeps past the spacecraft.

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6 HelioSwarm

Fig. 2: Single spacecraft missions only provide statistical properties of SW tur-

bulence averaged over both long times and diﬀerent kinds of turbulence. This

approach relies on Taylor’s hypothesis to map observed time series to advected

structures, measuring only a single 1D slice of the turbulence (red line in inset)

and thus only provides a crude measure of turbulent properties. Previous mul-

tipoint missions, e.g. MMS and Cluster, are only able to characterize spatial

structure at a single-scale. The HS observatory will encompass MHD and ion

scales scales simultaneously, enabling the characterization of multiscale struc-

ture and dynamics of turbulence in near-Earth plasmas. Adapted from [5] and

[34].

MHD theory adequately describes the inertial range spectral slope, but

provides no guidance in the critical higher-frequency transition connecting

inertial and dissipation ranges, which begins near the proton gyrofrequency

≡ Ω

/2π. At observed frequencies of f

break

∼ 0.33 Hz in the SW at 1 AU—

approximately equivalent to advected length scales of L

break

= v

break

∼

1200 km, the inertial range scale-invariance ends. This break arises before

sub-ion scales (e.g., ion gyroradius, ρ

), typically at apparent frequencies of

/ρ

∼ 3 Hz (length scales ∼ 100 km) [35]. In Figure 2 this breakdown is

seen as a change in spectral slope at the transition between inertial and dissi-

pation ranges. The spectral break suggests a change in the dominant physical

processes and a loss of cascaded energy. The energy removed from the cascade

is partitioned between the ions and electrons, with its dissipation leading to

the heating of these charged particles.

This process of turbulent dissipation is why SW plasma is much hotter than

simple theories of adiabatic expansion would predict [36]. If the SW were an

adiabatically expanding ideal gas, the protons at Earth would be much cooler

than observed [20] and protons at Jupiter orbit (∼ 5 AU) would be 8 times

cooler than at 1 AU, in contrast to Voyager observations [37]. Non-adiabatic

heating via turbulence dominates plasma thermodynamics throughout much

of the solar system, and is a leading candidate for accelerating the SW [38, 39].

The exact heating mechanisms leading to this heating are a matter of

substantial debate. Determining the nature of these mechanisms requires

observing 3D distributions of the turbulent ﬂuctuations. Plasma turbulence

is inherently anisotropic due to preferred directions associated with the IMF

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HelioSwarm 7

[11, 40], radial expansion[41] and large-scale gradients [42–44]. If turbulent

ﬂuctuations vary primarily parallel to the IMF (slab-like) [45], then non-

compressive, Alfv´enic ﬂuctuations would, at small scales, ultimately dissipate

energy via ion-cyclotron wave (ICW) heating [46]. However, for ﬂuctuations

that vary mostly perpendicular to the IMF (quasi-2D [47] or “critically bal-

anced” [48]), ICW heating is exceedingly weak. In this regime, dissipation

instead occurs via other mechanisms such as Landau damping [49] or stochas-

tic heating [50]. Recent work on imbalanced cascades [51, 52] complicates these

models by providing a pathway for low-frequency, anisotropic turbulence ﬂuc-

tuations to develop small scale structure parallel to the magnetic ﬁeld, enabling

dissipation via ICWs. If turbulent structures are highly anisotropic sheets,

they may undergo magnetic reconnection, which causes heating and particle

acceleration [53, 54]. To distinguish among these requires an accurate deter-

mination of the 3D power distribution. Previous determinations using single

spacecraft use long time series for suﬃcient statistics, [33, 55–57], combining

together intervals of turbulence with very diﬀerent properties. The regulation

of energetic particle transport, in both SW [58] and astrophysical plasmas [59],

is also sensitive to the turbulence spectrum and its anisotropies.

At a fundamental level, the nature of turbulent ﬂuctuations in magnetized

plasmas remains unknown: is it an MHD extension of hydrodynamic eddies

[32], a quasi-2D system [60], critically balanced wave-like ﬂuctuations [11, 48],

or a dynamically evolving mixture? The complexity of plasma turbulence pre-

cludes simple, analytic solutions. Numerical simulations are invaluable but

limited by incomplete physics and small system size[61]. Conﬁned laboratory

plasmas [62–64] have similarly limited scale separations and access to SW-like

physical parameters.

The SW is a natural laboratory where we can ﬁnally answer these ques-

tions by concurrently observing turbulent energy transfer and ion heating over

a targeted range of scales. However, single-spacecraft observations of SW tur-

bulence are fundamentally limited. Multi-spacecraft missions enabled advances

by creating geometric conﬁgurations to sample single-scale plasma structure

without relying on Taylor’s hypothesis (futher discussed in Section 3.1.1).

While four- (Cluster[65], MMS[66]) and ﬁve-spacecraft (Time History of Events

and Macroscale Interactions during Substorms (THEMIS)[67]) missions pro-

duce conﬁgurations that allow for single-scale measurements [68, 69], they still

cannot explore multiple scales simultaneously in three dimensions. Even with

advanced analysis techniques, scales sampled using four spacecraft cover at

most a factor of ∼ 10, as demonstrated for instance with the wave-telescope

technique [70, 71], nowhere near the > 2 orders of magnitude necessary to

simultaneously measure across inertial and dissipation ranges. HS’s conﬁgura-

tions created by 9 spacecraft provide the ﬁrst simultaneous multiscale view of

plasma turbulence, targeting key scales from MHD to sub-ion scales. By mea-

suring plasmas at multiple scales simultaneously, the HS Observatory promises

transformative impacts in our understanding of turbulence, which will be a

boon for heliophysics, astrophysics, and plasma physics [72–74].

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8 HelioSwarm

3 HelioSwarm Goals and Objectives

HS advances Goal 4 of the 2013 National Academy of Sciences (NAS) Helio-

physics Decadal Survey [1] (DS) which calls on the community to ”[d]iscover

and characterize fundamental processes that occur both within the heliosphere

and throughout the universe.” Magnetized plasma turbulence is the primary

mechanism responsible for transforming energy injected at largest scales into

small-scale motions, eventually dissipating as plasma heat. Plasma turbulence

is universal, responsible for energy transfer in such diverse systems as the solar

corona, SW, pulsar wind nebulae, accretion discs, interstellar medium, planet

formation regions, and laboratory fusion devices. Only the SW is both of suﬃ-

cient size for multiscale observations and accessible for in situ measurements.

Turbulence is identiﬁed as one of eight DS Goals for SW/Magnetosphere

Interactions (SWMI): “Understand the origins and eﬀects of turbulence and

wave particle interactions.” Because of that importance, turbulence is also

identiﬁed as a SWMI Decadal Imperative: “Implement...a multi-spacecraft

mission to address cross-scale plasma physics.” Likewise, the NASA Helio-

physics Roadmap [75] highlights “Understand[ing] the role of turbulence and

waves in the transport of mass, momentum, and energy” as one of its key

Research Focus Areas of high priority. Long standing heliophysics mysteries

— as how the solar coronal temperature increases by orders of magnitude and

how the SW is accelerated and heated — remain unanswered after decades of

research because we lack detailed understanding of how energy in turbulent

plasmas heat particles. HS advances these NAS and NASA science priori-

ties, and will speciﬁcally resolve six science objectives (O) associated with two

overarching science goals (G).

•

(G1) Reveal the 3D spatial structure and dynamics of turbulence in a

weakly collisional plasma.

– G1O1 Reveal how turbulence energy transfers in the typical SW plasma

as a function of scale and time.

– G1O2 Reveal how the turbulent cascade of energy varies with background

parameters in diﬀerent SW environments.

– G1O3 Quantify the transfer of turbulent energy between ﬁelds, ﬂows, and

proton heat.

– G1O4 Identify the thermodynamic impacts of intermittent structures on

protons.

•

(G2) Ascertain the mutual impacts of turbulence, variability, and bound-

aries near large scale structures.

– G2O1 Determine how SW turbulence aﬀects and is aﬀected by large-

scale structures such as Coronal Mass Ejections (CMEs) and Corotating

Interaction Regions (CIRs).

– G2O2 Determine how driven turbulence diﬀeres from that in undisturbed

SW.

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HelioSwarm 9

The HS goals and objectives in turn deﬁne the observatory and instrument

requirements, detailed in Secs. 4 and 5.

3.1 G1: Reveal the 3D spatial structure and dynamics of

turbulence in a weakly collisional plasma

Most of our limited present understanding of turbulence is based on sin-

gle point observations. Clusters of four spacecraft provide improvements by

exploring processes occurring at a single size scale at a single time. As any

three points deﬁne a plane, extraction of non-coplanar 3D information (such

as curls or gradients) requires four points and appropriate analysis methods

[76, 77]. However, turbulence is fundamentally multiscale; HS for the ﬁrst time

simultaneously explores the dynamics of processes at multiple size scales.

3.1.1 G1O1: Reveal how turbulent energy transfers in the

typical SW plasma as a function of scale and time

Using the undisturbed SW as a natural laboratory, with typical plasma param-

eters, HS measures ﬂuctuations in the plasma velocity and density (δv and δn)

and magnetic ﬁeld (δB) at MHD to sub-ion scales simultaneously using the

instrument suite described in Sec. 5. These data reveal how turbulent energy

is distributed and transferred as a function of space and time. Turbulent ﬂuc-

tuations are aﬀected by local magnetic ﬁelds [11, 47, 78, 79], so we must

characterize SW turbulence relative to the local IMF direction. Such studies

have been performed with data from single spacecraft; c.f. the review in Chen

(2016) [57], and necessarily rely upon the assumption of essentially frozen tur-

bulence structures, an approximation known as the Taylor hypothesis [80–83]

that neglects temporal variations and can infer only 1D variation along the

SW ﬂow direction. These studies also frequently assume that the turbulence is

insensitive to the angle between the SW velocity and the magnetic ﬁeld, using

variations in θ

to study the functional dependence of the turbulence on the

angle between the wavevector and magnetic ﬁeld θ

. Recent work [41] sug-

gests that this assumption may not be valid; verifying this claim will require

sampling the turbulent structures both along and transverse to the magnetic

ﬁeld direction simultaneously, a measurement that HS is designed to produce.

With HS, the Taylor hypothesis can be directly evaluated. Spectral infor-

mation is also available from proven analysis techniques (Sec. 6) such as

2-point correlations, structure functions, space-time correlations, and cascade

rate analysis [25, 33, 47, 55, 84–86], from which it is possible to extract

information about 3D spectral structure [84, 87, 88] and its intrinsic, scale-

dependent decorrelation times. These techniques frequently use measurements

of the velocity and magnetic ﬁelds directly, or the Elsasser variables (z

δv ±δb) [89] in which the magnetic ﬁeld is expressed in Alfv´en(velocity) units

(δb = δB/

√

) and δ indicates the use of a ﬂuctuating quantity.

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10 HelioSwarm

A prominent example of the use of Elsasser variables is the MHD 3

-order

law

∇ ·



∆z

∓

|∆z



= −4ϵ

, (1)

an analytic result involving spatial increments ∆x of the Elsasser ﬁelds

∆z

= z

(x + ∆x) −z

(x), and ⟨...⟩ denotes ensemble average. This relation

can be used to determine the energy cascade rate associated with the forward

and backward Elsasser ﬁelds ϵ

[87]. Formally, this requires knowledge of 3D

anisotropies. Previous studies have usually made assumptions about isotropy

[90–94] or only measured ϵ over limited range of scales [24]. HS can imple-

ment the isotropic form at all nine spacecraft, but also can integrate the 3D

form of the 3

-order law at several scales simultaneously, making use of all 36

spacecraft pairs to compute the 2-point spatial increments. HS provides simul-

taneous 3D multipoint knowledge needed to infer spatial gradients contained

in the 3

-order equation, quantifying directly those key terms for the ﬁrst

time, bypassing simplifying assumptions about isotropy, to measure cross-scale

energy transfer rates deﬁnitively.

No comprehensive observational evidence exists to distinguish between pro-

posed theories of turbulent energy transfer. A review of such theories can be

found in NAS 2020 Plasma Decadal Panel white papers [95–97] and other

reviews [11, 98]. Candidate energy transfer processes are related to relevant

dynamical timescales that include wave propagation, random and coherent

sweeping of small structures by larger structures, and nonlinear wave distor-

tion [99–103]. Numerical simulations provide insights regarding which of these

are important but results remain inconclusive due to fundamental limitations

associated with the necessary trade oﬀs between the volume of space simu-

lated and the physical processes included in the equations evolved. HS provides

observations to distinguish and reﬁne our understanding of the relevance of

these processes.

3.1.2 G1O2: Reveal how turbulent cascade of energy varies

with background parameters in diﬀerent SW

environments

Turbulence and plasma conditions in fast and slow SW diﬀer systematically in

terms of density, temperature anisotropy, and collisional age [7, 90, 91, 104–

106]. Slow SW turbulence is more highly variable in nature than the fast SW

[104] and due to its longer transit from the Sun, has more time to evolve

toward a fully developed state. These diﬀerences have been assessed in limited

fashion with single-point ([107, 108], e.g., Wind, Voyager) and single-scale [24]

(e.g., MMS) measurements. The varying SW speed is also associated with

variations in proton number density, temperature, alpha particle density, and

IMF strength. Plasma β = 8πnk

T/B

, the ratio of thermal to magnetic

pressure, a particularly important regulator of plasma processes [109], and

power imbalances (such as cross helicity σ

and residual energy σ

, [110]),

are also highly variable in the SW. These parameters inﬂuence the underlying

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HelioSwarm 11

energy cascade from MHD to sub-ion scales. HS targets to study the impact

of this variability on the dynamics of the turbulence.

3.1.3 G1O3: Quantify transfer of turbulent energy between

ﬁelds, ﬂows, and proton heat

Dissipation of turbulence is one of the most important factors inﬂuencing

heating and particle energization in the universe. Consequently, our goal of

investigating energy transfer must include how the cascade heats protons. Pro-

tons are of primary importance as they are the dominant species in terms of

both mass and momentum. How and how much energy is delivered to protons

via dissipation processes determines the overall partitioning of energy across

all species. Primary candidate mechanisms include: ICWs and cyclotron res-

onances [111]; Landau damping [49]; stochastic heating by large amplitude

turbulent ﬂuctuations [50]; and energization through intermittent structures,

including magnetic reconnection [112] and trapping in secondary magnetic

islands [113].

Current observations do not provide clarity. For example, intense ICWs are

commonly observed during times when plasma instabilities are present [114]

in extended “storms” during quiet SW and radial IMF [115]. Because ICWs

are capable of substantial heating of SW ions, it is important to understand

exactly how often they occur. ICWs may be omnipresent but can only be

detected by a single spacecraft when the SW ﬂow is aligned with the local IMF

(i.e., radial ﬁeld conﬁgurations). Applying methods such as the wave telescope

technique to HS observations, Sec. 6, will identify ICWs when the IMF is not

radial, thus establishing deﬁnitively whether ICWs are always present or not.

All aforementioned mechanisms occur at ion time and length scales and

create characteristic signatures in underlying proton velocity distribution func-

tions (VDFs); each mechanism deposits diﬀering fractions of energy to the

protons [50, 116, 117]. The absence or presence of these signatures reveals

which dissipation pathways operate; their relative strengths quantify their rel-

ative importance. Measurements of proton temperature at ion heating time

scales allows HS to quantify proton heating directly. One analysis method, col-

loquially referred to as ’PiD’, makes use of the measured pressure tensor Π

and ﬂow gradients S

= ∇

to compute the full pressure-strain interactions

Π : S which is the rate of production of proton internal energy [118]. These

methods are enabled in HS by simultaneous measurement of proton distribu-

tion functions and 3D multiscale turbulence, a combined capability lacking

in all previous missions. HS will allow us to directly quantify relationships

between the distribution of turbulence ﬂuctuations and transformation into

proton heat.

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12 HelioSwarm

3.1.4 G1O4: Identify thermodynamic impacts of intermittent

structures on protons

Intermittency is a universal property of turbulence in which dissipation pro-

cesses concentrate into small fractions of available volumes [119, 120], giving

rise to current sheet structures. Such structures have been studied in numeri-

cal simulations [121] and in situ observations [122]. Intermittency dramatically

impacts how turbulence heats plasma [123]. Cluster and MMS pioneered the

ability to resolve thin structures with 4-point curlometer and gradient tech-

niques [124, 125]. While revolutionary, such techniques probe only a single

scale at a time. HS provides combinatorically more spacecraft groupings and

simultaneous access to multiple scales, tremendously expanding 3D anisotropic

measures of intermittency with well-developed analysis tools, as described in

Sec. 6.

By measuring intermittency of turbulent ﬂuctuations at inertial and ion

scales simultaneously, HS diﬀerentiates between models of nonlinear coupling,

that predict enhanced amplitudes of Elsasser ﬂuctuations δz at small scales

compared to a scale-independent normal distribution of amplitudes. HS also

resolves the intermediate scales to provide further diﬀerentiation.

3.2 G2: Ascertain the mutual impacts of turbulence,

variability, and boundaries near large scale structures

While undisturbed SW is a pristine environment, disturbed SW occurs from

impacts of either large scale structures of solar or heliospheric origin or Earth’s

magnetosphere and provides diﬀerent environments to explore. Impacts are

mutual: turbulence can impact large-scale structures and boundaries and those

same structures can in turn change the nature of turbulence. Goal Two focuses

on these mutual interactions.

3.2.1 G2O1: Determine how SW turbulence aﬀects and is

aﬀected by large-scale structures such as CMEs and

CIRs

Passage of interplanetary coronal mass ejections (CMEs)[126] or corotating

interaction regions (CIRs)[127, 128] disturb the SW from its pristine state.

These large-scale features re-inject energy and thus modify SW turbulence.

While turbulence levels are reduced within CME structures, HS enables 3D

characterization of this (possibly weak) low-plasma β turbulence contained

within a large scale force-free structure. Near CMEs, driven turbulence departs

signiﬁcantly from that of the pristine SW; HS will diagnose 3D turbulence

modiﬁcations associated with diﬀusive shock acceleration [129] near fast CMEs

and waves driven by the CME’s propagation[130]. Passage of both CMEs and

CIRs through pristine SW turbulence allows us to explore diﬀerences in these

environments, enabling us to determine when and how speciﬁc energy transfer

and heating processes become important.

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HelioSwarm 13

3.2.2 G2O2: Determine how driven turbulence diﬀers from

that in undisturbed SW

The terrestrial bow shock, foreshock, and magnetosheath are permeated with

magnetic and plasma ﬂuctuations, strongly driving and modifying the tur-

bulent spectrum across inertial and dissipation scales both in amplitude and

shape[68]. These regions represent parameter regimes not accessible in pristine

SW. The dynamics in these locations are signiﬁcantly diﬀerent; for example,

ions reﬂected oﬀ the bow shock can lead to the self-generation of turbulence,

which takes the form of non-linear wave penetrating into the inner magne-

tosphere [131], while at the shock, turbulence generates high-speed jets that

regularly impact the magnetopause, resulting in dayside reconnection [132].

Turbulence is also seen to drive magnetic reconnection in these regions [133].

Finally, magnetospheric regions can be turbulent [134–137], but of a diﬀer-

ent nature (e.g. magnetically dominated) [138]. Objective Two explores this

variety of accessible systems to compare how driven environments diﬀer from

pristine SW.

4 HelioSwarm Observatory Design

The speciﬁc design of the HS Observatory is driven by decades of measurements

from near-Earth plasmas of characteristic length and time scales as well as

derived dimensionless parameters that are predicted to govern the behavior of

magnetized turbulence.

4.1 Quantities to be Measured

As discussed in Sec. 3.1.1, the primitive variables that describe magnetized

turbulence at MHD scales are the Elsasser variables [89] composed of magnetic

ﬁelds and particle densities and velocities. G1O1 requires measurements of

the IMF, SW proton density, and SW velocity. It must do so in undisturbed,

most-probable SW for which the range of proton densities is 1.6 to 20 cm

−3

and magnetic ﬁeld can be as large as 25 nT , but typically larger than 2.6 nT

(at the 90% occurrence rate) [35, 139]. To resolve at the lowest typical ﬁeld

strength, we require 10% resolution (0.26 nT), corresponding to 0.15 nT per

axis. Such measurements allow construction of Elsasser variables, needed for

magnetized turbulence analysis at each measurement location.

Measurements of the SW proton density, velocity and IMF must be made

at multiple points in 3D encompassing the turbulent cascade during aver-

age SW conditions, within large scale structure analysis intervals—equivalent

to approximately one hour long continuous observations— at cadences, time

knowledge, and sensitivities required to resolve and align SW and IMF

variations down to sub-ion scales.

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14 HelioSwarm

log

break

] (km)

log

[ρ

] (km)

(a)

−4

−3

−2

P[L

break

]

−4

−3

−2

P[ρ

]

1.5 2 2.5 3 3.5

1.5

2.5

3.5

10%

33%

50%

66%

90%

98%

90%

66%

50%

33%

10%

−4

−3

−2

300 400 500 600 700 800

(b)

Projected Performance

Instrument Requirement

’Fast’’Slow’

P[v

(km/s)]

(km/s)

−4

−3

−2

−1.2 −1 −0.8−0.6−0.4−0.2 0 0.2

FC iESA

SCM MAG

(c)

P[log

[ρ

(s)]]

log

[ρ

(s)]

10%

33%

50%

66%

90%

98%

10%

33%

50%

66%

90%

98%

Fig. 3: (a) Joint PDF of proton gyroradius ρ

and spectral break scale L

break

as measured by the Wind spacecraft at Earth’s L1 point [35, 139]. HS’s baseline

separations between spacecraft will cover from 3000 km to 50 km (blue box),

allowing the observatory to simultaneously measure MHD, transition, and sub-

ion physical processes in 85% of the pristine SW. (b) PDF of SW velocity

drawn from the same database, compared to FC instrumental requirements

and project performance, illustrating that HS will capture both typical and

extreme proton velocities. (c) PDF of the advected SW ion timescale ρ

compared to HS instrument cadences, demonstrating that HS will resolve the

IMF past ion-scales in nearly all the SW, and resolve both the ion-scale plasma

processes in typical SW conditions. In all panels, the red numbers indicate the

percentile of the cumulative distribution below the given value.

4.2 Spatial Resolution

To measure the multiscale nature of turbulence, HS’s baseline separations

between the nine spacecraft are designed to simultaneously span MHD scales

and ion kinetic scales, enabling the simultaneous resolution of MHD and

sub-ion processes and the transition between these scales, exempliﬁed by the

observed spectral break [84, 108, 109, 140–143] (see also Figure 2). Values

for these physical dimensions are empirically known from decades of SW

observations[35, 105, 139, 143]. Figure 3 shows the joint probability distri-

bution function (PDF) of the proton gyroscale ρ

and spectral break scale

break

= v

break

. These observations deﬁne three ranges: MHD scales at

> 1200 km; transition scales between 100 and 1200 km; and sub-ion struc-

tures < 100 km. HS’s baseline requirements are established to resolve these

characteristic scales simultaneously in 85% of the pristine SW, enabling the

Observatory to “encompass the turbulent cascade.”

4.3 Temporal Resolution

The Observatory measurement cadence and timing knowledge provide the tem-

poral resolution necessary to resolve advected SW structures. This analysis

requires measuring at time cadences from MHD scales down to the sub-ion

scales.

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HelioSwarm 15

Given the observed distribution of SW velocities, see Figure 3b, we can

calculate the ratio of the proton gyroscale ρ

to v

to construct an advected

proton timescale, Figure 3c, which plots the observed distribution against

instrumental measurement rates. The ﬂuxgate magnetometer (MAG) measures

at 16 samples per second (Sps) overlapping with the searchcoil magnetometer

(SCM, at 32 Sps) providing continuous coverage of larger and/or more slowly

advecting structures, while also resolving ion-scale structures traveling at the

fastest v

(∼ 800 km/s); The proton density (n) and velocity (v) are mea-

sured by Faraday cups (FCs) at a rate of 8 Sps, resolving ion scale structures

(∼ 100 km) traveling at typical speeds (400 km/s); Measurements of the pro-

ton temperature by the ion electrostatic analyzer (iESA) provide the necessary

context for the kind of turbulence HS is embedded in, with suﬃcient temporal

resolution to resolve changes in proton velocity distributions to help determine

the energy transfer processes associated with ion scale structure.

In order to resolve characteristic SW wave propagation directions across

multiple points, HS requires post-facto, relative pairwise separation knowledge

of 10% the separation distances. Timing requirements are driven by apply-

ing analysis methods described in Section 6 to synthetic data combined with

models for temporal uncertainty.

4.4 Observatory Stability

Simultaneous statistical analysis of turbulence (e.g. Sec. 6.1) requires not only

separations spanning the previous described spatial scales but also samples

taken over long enough periods of time to capture the nonlinear reshaping

of the underlying structures. One can calculate the correlation time scale τ

by determining the time lag necessary to reduce an autocorrelation of some

measured quantity F by 1/e from it’s zero-lag value

A [F (t), F (t + τ )] = ⟨F (t)F (t + τ)⟩ = ⟨F (t)F (t)⟩/e, (2)

where < ... > denotes an appropriate ensemble average. Analysis performed

on intervals measured within a correlation time are eﬀectively sampling the

same population of turbulent ﬂuctuations, and thus can be combined to study

the statistical properties of that plasma. Observations of the correlation time

scale in the SW[144, 145], illustrated in Figure 4, typically ﬁnd it ranges from

tens of minutes to approximately an hour. This duration of SW data provides

robust turbulence analysis yet is short enough to eﬀectively sample the same

parcel of SW. These observations drive the timescales over which the observa-

tory spacecraft separations need to be constant, a requirement the HS Design

Reference Mission (DRM) satisﬁes, enabling the accrual of usable intervals for

the application of analysis approaches outlined in Sec. 6; the average relative

change in the vector baselines increases slowly in time (red line), reaching 0.7%

at 60 minutes and 1.5% at 120 minutes.

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16 HelioSwarm

−4

−3

−2

1 1.2 1.4 1.6 1.8 2 2.2

P[Correlation Time]

|λ(t

)−λ(t

|λ(t

[%]

log

[Time (min)]

1 Hour

−1000

1000

−1000 0 1000

Time (min)

GSE

(km)

GSE

(km)

S/C Relative

Positions

10%

33%

50%

66%

90%

98%

100

120

140

160

Fig. 4: PDF of correlation time measured by ACE (left panel) [144] compared

to the average change in HS DRM baseline separation magnitudes as a function

of time (red line). At right, the x

GSE

− y

GSE

projection of the evolving Node

positions relative to the Hub, with color indicating time since apogee; the

signiﬁcant overlap in positions illustrate the relative stability of the observatory

conﬁguration.

# Spacecraft 4 5 6 7 8 9 10 11

Baselines 6 10 15 21 28 36 45 55

Tetrahedra 1 5 15 35 70 126 210 330

Polyhedra 1 6 22 64 163 382 848 1816

Table 1: Number of baselines, tetrahedral, and polyhedral (with at least four

vertices) conﬁgurations that can be constructed from N Spacecraft.

4.5 Spatial Conﬁgurations

In conjunction with spatial separation requirements, the application of the

analysis approaches in Sec. 6 require speciﬁc spatial conﬁgurations. Given N

spacecraft, there are N(N −1)/2 distinct pair-wise baseline separations. Sim-

ilarly, for N spacecraft, one can construct





4!(N−4)!

unique tetrahedral

conﬁgurations, or

i=4





polyhedral conﬁgurations with at least four ver-

tices. The number of baselines, tetrahedra, and polyhedra are tabulated as a

function of the number of spacecraft in Table 1. The orientation and geome-

tries of these conﬁgurations have been carefully tailored so that they span the

appropriate size-scales and directions to address the mission objectives, as dis-

cussed in the following subsections and illustrated in Fig. 5. Determining when

the HS Observatory satisﬁes these conﬁgurational requirements is character-

ized in 1-hour units, during which baseline separations are eﬀectively constant,

see Fig. 4. The number of hours satisfying these requirements are laid out in

Table 2.

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HelioSwarm 17

(km)

-60

-30

-60-30 0 30 60

GSE

Solar Wind

Magnetosphere

Foreshock

-30

-60-30 0 30 60

GSE

100

500

1000

1500

2000

0 0.3 0.60.9 1.2

` P

L(km)

# s pacecraft

´1000

0 1000

´1000 0 1000

Hour 2472

The HelioSwarm Observatory:

Phase-B Design Reference Mission

GSE

(km)

GSE

(km)

´1000

0 1000

´1000 0 1000

GSE

(km)

GSE

(km)

´1000

0 1000

´1000 0 1000

GSE

(km)

GSE

(km)

3D Conﬁguration

MHD

Transition

Kinetic

Observatory

Moon

REGULAR

Polyhedral

Conﬁguration

Hub Nodes

Fig. 5: Summary plot of HelioSwarm Observatory Phase-B DRM positions

and separations. Top Row Relative positions between the Hub (red) and eight

Nodes (black) projected into the GSE co¨ordinate system at hour 2472 from

the DRM. Bottom Left Projected vector components of the 36 inter-spacecraft

baseline separations (black dots) demonstrate coverage of MHD and ion-kinetic

scales, as well as the transition region in-between. The lunar resonant orbit of

the observatory (black dot) in the GSE co¨ordinate system is shown as colored

lines in the upper-right inset, with the moon’s location (open circle) included

to illustrate scale. Times with orthogonal coverage over all three scales, high-

lighted in color, arise in the pristine SW (red lines), the magnetically connected

SW (green) and the magnetosphere/magnetosheath (blue). Bottom Right The

size and geometric conﬁgurations of the polyhedra constructed by spacecraft

subsets of the HelioSwarm observatory. The number of spacecraft is indicated

by color, while the size of the polyhedra L and its regularity (the RMS of

the elongation E and planarity P ) are indicated on the ordinate and abscissa

respectively. The times when there are at least two regular polyhedra with

characteristic sizes more than a factor of three diﬀerent are indicted in the

upper inset, using the same color scheme as the 3D Conﬁguration inset. As

quantiﬁed in Table 2, due to the high eccentricity of the orbit, the Observa-

tory samples these regions near apogee for a substantial fraction of the orbit

period. A video of the HS DRM Geometries throughout the Science Phase is

available in Online Resource 2.

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18 HelioSwarm

4.5.1 3D Conﬁgurations

To calculate cascade rates, correlation scales, and structure functions to char-

acterize the multiscale and 3D nature of turbulence, the 36 unique baselines

between HS’s nine spacecraft have vector components spanning three orthog-

onal directions along, transverse, and normal to the Earth-Sun line (Radial,

Tangential, Normal (RTN) co¨ordinates) with amplitudes covering MHD, tran-

sition, and sub-ion scales, while simultaneously the magnitudes of the baseline

vectors also span these three ranges of scales. These 3D conﬁgurations, illus-

trated in Figure 5, resolve variations along and across the local magnetic ﬁeld

and ﬂow directions, necessary for verifying theories of anisotropic turbulent

transfer and distribution of energy.

4.5.2 Polyhedral Conﬁgurations

The polyhedral conﬁguration is satisﬁed when at least two of HS’s constituent

polyhedra, each satisfying

√

+ P

≤ 0.6, have at least a factor of three

diﬀerence in L, simultaneously measuring the spatial structure of turbulence

at multiple scales.

HS conﬁgurations are also designed for multi-point analysis techniques

which determine spatial gradients and distributions of power (e.g., wave-

telescope, curlometer, and related gradient analysis techniques [76, 77]. Spatial

gradient methods require the SC be arranged in a quasi-regular fashion,

occupying vertices of pseudo-spherical polyhedra. One can characterize the

geometry of these polyhedra by calculating the eigenvectors of the volumetric

tensor

R =

α=1

− r

) (r

− r

)

(3)

where r

α=1

is the mesocenter of the conﬁguration, and r

rep-

resents the positions of the individual SC. The square roots of the three

eigenvalues of R represent the major, middle, and minor semiaxes of the con-

ﬁguration, a, b, and c. These values can be interpreted directly by deﬁning a

characteristic size L = 2a, as well as the elongation E = 1 −

and planarity

P = 1−

. Figure 6 illustrates the distribution of polyhedra from a single hour

of the HS Observatory conﬁguration. Polyhedra with small elongation E and

planarity P,

√

+ P

≤ 0.6, can be used to accurately measure structure

of sizes on the order of the characteristic size L [71, 146]. HS’s 9 spacecraft

produce 382 polyhedra with at least 4 vertices, the minimum needed for 3D

analysis techniques, and at many diﬀerent scales. Additionally, HS has con-

ﬁgurations where at least two pseudo-spherical polyhedra exist with at least

a 3:1 ratio in L. These formations, referred to as polyhedral conﬁgurations,

simultaneously measure spatial structure of turbulence at multiple scales.

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HelioSwarm 19

0.25

0.5

0.75

0 0.25 0.5 0.75 1

L (km)

Planarity (P)

Elongation (E)

Hour 2474

100

1000

Pseudo

Sphere

Potato

Pancake

Sausage

Knife

Fig. 6: The distribution of planarity (P), elongation (E), and characteristic

size (L, with blue and red representing the smallest and largest scales respec-

tively) of all 382 polyhedra with at least 4 vertices for the HS DRM at an

arbitrarily selected hour 2474. The diﬀerent regions in E-P space are labeled to

characterize the geometries of these polyhedra. The Observatory trajectories

are designed to have multiple pseudo-spherical polyhedra with signiﬁcantly

diﬀerent sizes to enable measurements of spatial structures at MHD- and ion-

scales simultaneously.

4.6 Observatory Orbits

The HS Observatory accesses the near-Earth regions of interest with a 2-

week, lunar-resonant, high Earth orbit (HEO) [147–150]. The HS Observatory

design and onboard propulsion produce inter-spacecraft separations both along

and across the Sun-Earth line. The Nodes perform routine trim maneuvers to

maintain customized conﬁgurations that satisfy the 3D and Polyhedral require-

ments over the mission lifetime. Since the science orbit is nearly inertially

ﬁxed (with a low rate of apsidal precession), the apogee rotates through the

SW, foreshock, and magnetosphere-dominated regions as the Earth completes

a single orbit of the Sun. This progression allows the Observatory to sample

the pristine SW and regions of strongly driven turbulence during the 12-month

Science Phase, addressing both G1 and G2.

Given an empirical model for the extent of the magnetosphere [151] and

the average orientation of the IMF combined with the phase B DRM trajecto-

ries, the HS Observatory spends thousands of hours in the required near-Earth

regions of interest, with hundreds of hours in both of the required spatial con-

ﬁgurations in each region; see Table 2 for summary of hours and Figure 5

for an illustration of the residence time in the regions. Measurements from

all instruments are recorded throughout the orbits outside of thruster oper-

ations, eclipses, and calibration activities and transmitted regardless of the

Observatory conﬁguration.

4.7 Mission Duration

As discussed in Sec. 3.1.2, SW parameters drive the behavior of turbulence,

and more extreme values of these parameters are useful for distinguishing com-

peting theories. To establish the minimum number of hours needed for HS

science data suﬃciency, we note that ∼ 10 hours in extremely high (≥ 10)

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20 HelioSwarm

Phase B DRM; LRD 2028 Fig. 5 Total 3D Polyhedral

Solar Wind Red 2881 777 1068

Foresho ck Green 2470 977 852

Magnetosphere/Magnetosheath Blue 3149 650 639

Science Phase 8850 2404 2559

Objective Total 3D Polyhedral

Pristine SW G1O1 2015 544 747

Extreme SW G1O2 58 16 21

SW w/ Large Scale Structure G2O1 546 147 202

Strongly Driven Turbulence G2O2 5619 1627 1491

Table 2: HS measures thousands of hours in targeted near-Earth regions of

space, with hundreds of hours in optimal polyhedral (Sec. 4.5.2) and 3D con-

ﬁgurations (Sec. 4.5.1) for the application of analysis approaches outlined in

Sec. 6, providing measurements to advance the understanding of turbulence in

typical (G1O1,G2O2) uncommon (G2O1) and extreme (G1O2) plasma condi-

tions.

and low (≤ 0.1) plasma β enabled strong characterization of the spectral

break, diﬀerentiating between predicted dissipation mechanisms [109]. Using

this assessment, the required number of hours of observation for the Baseline

Mission was developed by analyzing two decades of Wind [35, 139] data to

ensure that we would adequately sample the full range of SW variability. Our

methodology was to generate PDFs of parameters controlling turbulent behav-

ior, e.g. SW speed (v

), plasma beta (β), proton temperature (T

), balance

of power between Sunward and anti-Sunward propagating ﬂuctuations (cross

helicity, σ

[152]), diﬀerence between kinetic and magnetic energy (residual

energy σ

[110]), SW collisionality (Coulomb number N

[153, 154]), and

Alfv´en Mach number (v

). Obtaining ∼ 10 hours of measuring turbu-

lence at relatively large and small values of these parameters determines the

overall requirements for the number of hours in polyhedral and 3-D conﬁgura-

tions; from the widths of the parameter PDFs, we determined that measuring

500 (100) hours in the 3D (polyhedral) conﬁguration in the pristine SW, which

then result in HS measuring 10 (2) hours of turbulence with extreme param-

eters both higher than the 98th percentile and lower than 2nd percentile of

those values (corresponding to β ∼ 0.1 and β ∼ 10 [109]), a suﬃcient num-

ber of intervals at the very most extreme parameters to accomplish Mission

science. Magnetosheath plasmas that will also be measured by HS typically

have even higher values of β

∥,p

[138]. Measurements of these extreme intervals

allow for the identiﬁcation of diﬀerent turbulent processes that are preferred

in diﬀerent parameter regimes, and will also be useful for providing accessible

analogies to astrophysical systems where the thermal pressure dominates, e.g.,

the ISM (β

∥,p

≳ 10) or accretion disks (β

∥,p

≳ 1).

Large scale structures (LSS) generated by the Sun– e.g., CMEs, or produced

as the SW propagates, e.g., CIRs can drive diﬀerent kinds of turbulence com-

pared to SW w/o LSS. By using in situ SW measurements of these structures

over the last two solar cycles [126, 128], we calculate the ﬁlling fraction during

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HelioSwarm 21

the 12-month Science Phase of these two kinds of structures for a 2028 Launch

Readiness Date (LRD) based upon equivalent phases from Solar Cycles 23 and

24; the total anticipated LSS hours for this LRD are tabulated in Table 2.

The average CME ﬁlling fraction is 2.15% (1.9%/2.4% in Solar Cycle 23/24)

while the CIR ﬁlling fraction is 16.8% (19.8%/13.8% in Solar Cycle 23/24).

These rates correspond to 62 hours of CME observations, with 16/23 hours

in 3D/polyhedral conﬁgurations and 484 hours of CIR measurements, with

131/179 hours in 3D/polyhedral conﬁgurations. We have repeated this exercise

for other LRDs, and found that regardless of launch date, there will be a

suﬃcient number of hours of observed CMEs and CIRs to provide data to

bring closure to G2O1.

4.8 Resilience, Redundancy, and Robustness of

Multi-satellite Observatory

Multi-SC swarm design oﬀers innovations in ﬂexibility and reconﬁguration of

the observatory. Orbital mechanics forces create continuously evolving relative

positions among the 9 SC in HS. With known exceptions, the nominal swarm

conﬁguration has redundancy in most of the 3D baselines and tetrahedral

vertices and accrues successful hours of science data collection well above the

requirements.

Robustness above required performance and redundancy in spatial conﬁg-

urations create resilience in the event of contingencies. For the case of the loss

of any one (or two) Nodes, the required number of hours in both conﬁgurations

can be achieved within the duration of the 12-month Science Phase through a

repositioning of the remaining Nodes to construct the conﬁgurations for which

suﬃcient hours have not been achieved.

4.9 Place within the Heliospheric System Observatory

HS stands alone, but would also be part of the Heliospheric System Observa-

tory (HSO) which provides additional opportunities for joint mission studies.

Parker Solar Probe (PSP) [155] and Solar Orbiter (SolO) [156] are making

high-cadence plasma and IMF measurements of the innermost heliosphere.

These inner-heliospheric missions provide only single point measurements, but

these inform limits on injection scale structures that cascade into smaller struc-

tures as they propagate to 1 AU. Together with HS, and supplemented by

Polarimeter to UNify the Corona and Heliosphere (PUNCH) imaging[157],

these observations allow for estimates of 1-AU-scale evolution and radial

and longitudinal gradients. At intermediate scales (10

km), HS observations

in combination with other missions in the HSO positions near the Sun-

Earth L1 point (e.g., Advanced Composition Explorer (ACE)[158], Wind[159],

Interstellar Mapping and Acceleration Probe (IMAP)[160], Deep Space Cli-

mate Observatory (DSCOVR)[161]) provide opportunity for long-baseline

correlations and to address the long-open question of local geometries of inter-

planetary shocks and ﬂux ropes. These same HSO missions provide additional

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22 HelioSwarm

SW composition information to augment HS alpha particle measurements.

Conjunctions with MMS[66] may also prove useful in extending the range of

scales over which energy transfer and dissipation can be studied. Finally, given

that energetic particle propagation is impacted by SW turbulence, ACE, Wind,

Solar Terrestrial Relations Observatory (STEREO), and IMAP energetic par-

ticle measurements can test the eﬀect of turbulence models and mechanisms

HS quantiﬁes. Joint study opportunities will depend on what HSO assets are

operating when HS launches, but the breadth of the positions and instrumen-

tation of missions within the HSO will enable a variety of examinations of

fundamental processes at play in our Heliosphere.

5 HelioSwarm Mission Implementation

HS was selected as a Heliophysics Division Medium Explorer (MIDEX) mission

by NASA Science Mission Directorate in 2022, and is currently in the formula-

tion phase. MIDEX missions are aﬀordable testbeds for ﬂagship science, from

a cost and risk implementation perspective. The HS hardware and operations

approach are all extremely high heritage to minimize overall project risk.

The HS architecture consists of one central Hub, an ESPA-class (EELV

Secondary Payload Adapter) spacecraft provided by Northrop Grumman, and

eight co-orbiting Nodes, SmallSats provided by Blue Canyon Technologies,

both high heritage, 3-axis stabilized spacecraft. The Hub, Sec. 5.5, carries the

eight Nodes to the science orbit. Pairs of Nodes will then separate from the

Hub over four consecutive 14-day orbits. Each Node, Sec. 5.6, possesses identi-

cal instrument suites (IS) consisting of three high-heritage, high-TRL sensors

optimized for HS: the Faraday Cup (FC, Sec. 5.2), provides high cadence mea-

surements of the SW density and ﬂow, the Fluxgate Magnetometer (MAG,

Sec. 5.1.1), and Search Coil Magnetometer (SCM, Sec. 5.1.2), provide mea-

surements of the IMF at cadences suﬃcient to probe ﬂuctuations from MHD

to sub-ion scales. The Hub has the same IS as the Nodes, plus an ion Electro-

static Analyzer (iESA, Sec. 5.3), another high-heritage, high-TRL instrument

that will provide high cadence measurements of the proton and alpha particles

in order to characterize the local turbulence and to quantify ion heating. An

electron Electrostatic Analyzer, Sec. 5.4), included as a Student Collaboration

Option for installation on the Hub, provides additional context for the plasma

environment sampled by the HS Observatory.

The instruments were speciﬁcally selected to be both capable of address-

ing the science objectives when used as an Observatory and for having high

heritage to ensure the fabrication, integration, and testing approaches for the

required nine copies of ﬂight model instruments, along with their costs and

schedules, would be low risk.

5.1 Magnetometers

HS uses a combination of ﬂux gate (MAG) and search coil (SCM) magne-

tometers to measure the IMF over the required frequency range indicated by

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HelioSwarm 23

Observable Requirement Projected Performance Instrument

Multi-point vector DC to 2-Sps DC to 16-Sps MAG

DC IMF B ±100nT ±128nT (all SC)

0.15 nT per axis 0.1 nT per axis

Multi-point vector 0.1 to 32-Sps up to 32-Sps SCM

AC IMF B 15/1.5 pT/

√

Hz at 1/10 Hz 6/0.6 pT/

√

Hz at 1/10 Hz (all SC)

Multi-point 0.15 s 0.125 s FC

proton density n

0.2 - 20 cm

−3

0.1 - 50 cm

−3

(all SC)

±6% ±5%

Multi-point 0.15 s 0.125 s FC

proton velocity v

250 - 800 km/s 212 - 840 km/s (all SC)

±3% Accuracy ±1%

Single-point 0.3 s 0.15s iESA

proton temperature T

− 5 × 10

K 10

− 10

K (Hub)

±5% ±1.8%

Single-point temperature 0.3 s 0.15s iESA

anisotropy

⊥

∥

0.2 − 5 0.1 − 10 (Hub)

±6% ±3.4%

Single-point α-proton Hourly Averages 10 s iESA

density ratio

0 − 40% 0 − 100% (Hub)

±10% ±3.4%

Table 3: Plasma and magnetic ﬁeld observables measured across the HS

Observatory. Required cadences, ranges, and accuracy for the measurements,

as well as the projected performance and the instrument that will provide the

measurement are organized by column.

Figure 2 (DC ∼ 3600 s to sub-ion < 0.15 s). Two diﬀerent magnetometer types

are required owing to sensitivities required, especially at high frequencies (15

pT/ Hz at 1 Hz and 1.5pT/ Hz at 10 Hz – see noise ﬂoors on Figure 2);

these same sensitivities impose mission requirements for DC and AC magnetic

cleanliness. The MAG and SCM instruments overlap in frequency allowing for

cross-calibration and the production of a merged data product, as has been

performed for other missions [162, 163].

5.1.1 Flux Gate Magnetometers (MAG)

The MAG is a dual core ﬂuxgate magnetometer designed and built by Imperial

College London (Imperial) which will be carried on every HS SC to measure

the local magnetic ﬁeld. The MAG design is based on direct heritage from

the successful Solar Orbiter [164] magnetometer (Fig. 7) with modiﬁcations

taken from the soon-to-ﬂy JUICE (JUpiter ICy moons Explorer) instrument.

HelioSwarm MAG will carry just one sensor on each spacecraft, at the end of

a dedicated 3 m boom to minimise the eﬀects of spaceraft ﬁelds, connected to

the instrument electronics box via a harness. The electronics box will contain a

power supply and Front End Electronics board: the latter will drive the sensor

and digitise the signal, sending it directly to the spacecraft digital processing

unit (DPU) where it will be ﬁltered and decimated to 16 vectors/s on a common

timeline with the SCM.

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Fig. 7: MAG is based on the ﬂight-proven Solar Orbiter magnetometer design.

MAG operations are straightforward, with the instrument operating

throughout the science orbit. The instrument will have a 4 pT resolution in its

most sensitive range of ±128 nT but can range automatically up to 60, 000 nT

and can therefore operate in a full Earth ﬁeld before launch.

MAG data will be calibrated at Imperial College, with inter-calibration

between S/C performed to ensure that derived products such as volumetric

currents are reliably estimated. MAG therefore contributes directly to the

multi-point vector magnetic ﬁeld measurement observable in Table 3, but is

also central to the AC magnetic ﬁeld measurement as well as some plasma

products such as temperature anisotropies.

5.1.2 Search Coil Magnetometers (SCM)

The SCM is a heritage set of magnetic sensors designed and built by Labora-

toire de Physique des Plasmas (LPP) and Laboratoire de Physique et Chimie

de l’Environnement et de l’Espace (LPC2E) selected to measure the IMF’s

higher frequencies needed to capture advected ion-scale structures. The HS

SCM design is based on the most recent sensor developed for the ESA JUICE

mission by LPP [165–167]. LPP and LPC2E will be responsible for the testing

and calibration of the instruments.

The SCM consists of a tri-axial set of 20 cm long magnetic sensors with

associated preampliﬁer (ASIC) mounted at the tip of a 3 m boom opposite to

the MAG boom. Each sensor axis consists of two windings (a primary and a

secondary) around an internal PEEK mandrel inside which the ferromagnetic

core (mu-metal) used on other ﬂight heritage missions, (e.g. Cluster [168] or

THEMIS [169]) resides. Windings are connected to the preampliﬁer which

drives the analog signal down the SCM boom harness to the IDPU which

performs the digitization. SCM ground calibration is performed at the National

Magnetic Observatory of Chambon-la-forˆet using a facility upgraded by LPP

for MMS and BepiColombo.

Each primary winding response is modiﬁed through a ﬂux-feedback applied

via a secondary winding to produce the frequency response and phase stability

needed for Observatory-level analyses.

SCM has a single science operational mode drawing a steady 0.3 W. The

three diﬀerential analog outputs of the SCM preampliﬁer are anti-alias ﬁltered

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HelioSwarm 25

Fig. 8: JUICE SCM heritage instrument with its ASIC preampliﬁer.

and digitized by the IDPU receiving electronics at 128 Sps then ﬁltered to

32 Sps to satisfy HS observational requirements described in Table 3. This

science operational mode is only interrupted during the in-ﬂight calibration

sequence. This sequence, scheduled for one per orbit and following events such

as maneuvers and eclipses, will follow procedures successfully implemented on

MMS, PSP, and SolO. It is performed to assess the stability of the transfer

function through the mission using a calibration signal provided by the IDPU.

5.2 Faraday Cups (FC)

The Faraday Cup (FC) is a heritage-based design developed at the Smith-

sonian Astrophysical Observatory (SAO), in conjunction with University of

California, Berkeley (UCB), and Draper Laboratories. The sensor makes mea-

surements of the radial VDFs of SW ions along with the ﬂow angle of the

incoming beam to measure proton densities and velocities over the ranges and

sensitivities typical of the pristine SW.

Previous Faraday Cups have been employed on a wide variety of missions

including Voyager [170], Wind[171], DSCOVR[161], and PSP[172, 173]. Two

of the HS FC electronics boards (the logic/signal analysis board and the low-

voltage power supply) are direct copies of the PSP electronics. A third board

(the high-voltage power supply) is a fully-qualiﬁed backup design from the PSP

instrument development. The instrument uses an oscillating electric poten-

tial to create an electric ﬁeld that accepts or rejects particles based on their

energy/charge. Particles with large enough E/q to successfully transit the elec-

tric ﬁeld deposit their charge onto collector plates that measure the incoming

current of SW particles.

A Faraday Cup instrument is placed on the sun-facing side of each space-

craft so that an unimpeded view is maintained in the direction of the Sun.

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Fig. 9: The Faraday Cup mechanical design (as of the concept study report).

The mounting bracket is displayed in a semi-transparent mode. The instrument

consists of two main subassemblies: the sensor (the top cylindrical section)

and the electronics module (the lower rectangular box), which are connected

by ﬂexible coaxial cables.

Because Elsasser analysis involves measurements from both the IMF and

SW, cross-sensor timing, pointing, and alignment requirements between the

magnetometers and FC are levied.

The Faraday Cup operates in a single operational conﬁguration throughout

all phases of the mission. The instrument starts at its lowest voltage (ener-

gy/charge) and steps its way upward through 16 voltage windows while making

measurements of the incoming SW current on each of its four collector plates in

each window. The instrument keeps track of the maximum current measured

in the previous spectrum so that the following spectrum can be measured with

a more focused voltage range with better resolution.

The FC instrument design parameters have been determined by analyz-

ing the historic distribution of all measurements made by the Wind Faraday

Cup instrument. The aperture sizes, voltage ranges, and ﬁeld-of-view for the

HelioSwarm instrument are designed to capture more than 98% of the SW

conditions (velocities, densities, and temperatures) that have been previously

observed. The resulting voltage range will allow for measurement of proton

velocities in the range of about 200-850 km/s.

The Faraday Cup instruments provide a measurement of the radial dis-

tribution functions of the SW plasma on each of the nine spacecraft along

with plasma quantities derived from those distributions. By calculating the

moments of the distribution and by ﬁtting an assumed functional form to the

distribution, the vector velocity, density, and radial temperature can be pro-

vided. These data products contain 8 measurements per second and fulﬁll the

multi-point measurement requirements of the velocity and density of the SW,

as shown in Table 3.

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5.3 Ion Electrostatic Analyzer (iESA)

The iESA is a particle sensor designed and built by Institut de Rescherch

en Astrophysique et Planetologie (IRAP, Toulouse, France), Laboratoire

d’Astrophysique de Bordeaux (LAB, Pessac, France), University of New Hamp-

shire (UNH, USA), and Mullard Space Science Laboratory (MSSL, UK), with

IRAP technical leadership and heritage. The direct heritage instrument is the

Proton and Alpha Sensor [174] onboard the Solar Orbiter mission [175], with

some sub-systems inherited from other past particle instrumentation led by

IRAP (on STEREO, MAVEN, Cluster, etc.). iESA measures the full proton

and alpha particle distribution functions with an unprecedented combination

of high energy, angular and time resolutions (cf. Table 3).

As illustrated in Figure 10, entrance deﬂectors allow for the sweeping of

input elevation angles ±24

◦

from the main detection plane with 3

◦

angular

binning, which is resolvable with the use of a collimator. The deﬂected and

collimated ions are then subject to E/q selection through a classic top-hat

electro-static analyzer. The E/q selected ions are focused onto the main detec-

tion plane, which comprises 16 channel electron multipliers (CEMs). These

perform a 10

gain in charge collection on anodes with 3

◦

resolution in azimuth

over an angular range of ±24

◦

as well, allowing for a homogeneous ±24

◦

ﬁeld-

of view with 3

◦

angular resolutions, in both elevation and azimuth angles.

The iESA electronics contains (1) a front-end board comprising 16 CEMs with

associated anodes and ampliﬁcators, (2) a high-voltage board to supply the

entrance deﬂectors, analyzer plates, and CEMs with the required (static or

sweeping) high voltages, as well as (3) an FPGA and (4) a low-voltage power

supply board dedicated to instrument control and power.

iESA operations are based on the sequential stepping of the electrostatic

analyzer and entrance deﬂector high voltages. The instrument implements SW

beam-tracking strategies [174], using previous measurements, to dynamically

set the energy and angular bins of the next sample, allowing for faster mea-

surement cadence. The iESA is highly versatile and the tracking strategy can

implement any combination of energies and angles. Instrument operation will

be adapted to the science target, but a primary operation mode is expected to

be a Proton Tracking mode measuring the 3D VDFs of SW protons with high

energy (8%) and angular (3

◦

) resolutions at a cadence down to 150 ms, well

into the sub-ion timescales. To characterize alphas, a Proton-Alpha Tracking

mode will be used, with 48 energy bins and a 450 ms cadence, though longer

accumulation times can be used to enhance counting statistics as needed.

5.4 Student Electron Electrostatic Spectrograph Student

Collaboration

In addition to the magnetic ﬁeld and ion instruments previously listed in

this section, HS has also proposed to include a Student Electron Electrostatic

Spectrograph (SEE) Student Collaboration project to measure ambient, low

energy electrons. This electron instrument would be mounted on the Hub SC,

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28 HelioSwarm

Fig. 10: iESA subsystem components (as of the concept study report), include

the deﬂectors, collimators, and analyzer spheres (top), as well as the 16 channel

electron multipliers, front end electronics, low- and high-voltage power supply,

and FPGA board.

and would be used to study the connectivity of the local magnetosphere, solar

wind, and cis-lunar space via measurements of low-energy electron popula-

tions. The project would be co-led by graduate and undergraduate students,

with the prime deliverable from the SEE project a cohort of future scientists

educated in the lifecycle of a NASA mission, including instrument develop-

ment and merger of science goals with hardware design. A backup design for

SEE has PSP and ESCAPADE ﬂight heritage [176].

5.5 The Hub

Northrop Grumman (NG) provides the Hub spacecraft. This ESPA-class

spacecraft serves as the central relay for all Nodes within the Observatory and

is based on the high-heritage ESPAstar line which was designed to carry sepa-

rable payloads to orbit. The Hub is 730 kg at launch, including the hydrazine

propellant necessary for carrying it and all the Nodes into the HS science orbit,

illustrated at the top of Fig. 11. The Hub is capable of generating 1165 W of

power via its single deployable solar array. As conﬁgured for science, the Hub

spans a maximum dimension of 8.4 m.

5.6 The Nodes

The Node spacecraft are Blue Canyon Technologies (BCT) Venus-class space-

craft with standard accommodations for hosting the HS payload. As conﬁgured

for HS, the SmallSat Nodes are just over 70 kg each and use onboard propul-

sion to maintain the proper swarm geometry. The Nodes generate 200 W of

power and provide a single mechanical interface to the HS payload. With

booms deployed, bottom left of Fig. 11, the maximum tip-to-tip dimension of

the Nodes is just over 6m.

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HelioSwarm 29

Fig. 11: Transfer (top) and Science (bottom) Conﬁgurations for the Hub

(Sec. 5.5) and Node (Sec. 5.6) S/C.

5.7 Observatory Architecture

The HS ﬂight system will launch with the Hub carrying all 8 Nodes through a

series of phasing loops and a lunar swingby into the science orbit over a period

of approximately 72 days. Once the science orbit (a High Earth Orbit P/2 lunar

resonant orbit with apogee greater than 60R

and perigee less than 12R

pairs of Nodes are separated from the Hub spacecraft and instrument checkouts

and calibrations occur during the ≈ 81-day commissioning phase. Once the

Nodes have been maneuvered into their proper locations in the observatory,

the 12-month science phase begins. HS uses a Hub-and-spoke communications

architecture in which the Hub is the only direct link to the ground (via S-

band, DSN) and each Node receives commands from and relays science data

directly to the Hub via S-band crosslinks.

The Mission Operations Center (MOC) is hosted out of ARC, with engi-

neering support centers for Hub and Nodes at NG and BCT respectively. The

Science Operations Center (SOC) is hosted out of the PI-institution, UNH,

which is also responsible for delivering L1-L4 data products to NASA SPDF;

see Sec. 5.8. The HS missions operations approach strategically uses the inher-

ent orbital dynamics of the observatory; the swarm naturally “expands” and

“contracts” over each 14-day orbital period. The Flight Dynamics team has

designed the staggering of the Node-Hub closest approaches around perigee

to facilitate periods of high-rate data downlink for each Node each orbit. As

the observatory begins to expand out towards apogee, the polyhedral perfor-

mance, Sec. 4.5.2, requirements are satisﬁed. At apogee and on the contraction

back in towards perigee, the longest-baseline 3D performance requirements are

satisﬁed, Sec. 4.5.1.

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5.8 Data Processing and Selection

The Science Data Center (SDC) at the UNH SOC supports HS data processing,

produces timing and other ancillary data that are provided to the instru-

ment teams, releases and archives L0-L4 data with associated calibrations, and

provides data selection tools to the community.

Automated processes transfer L0 telemetry data from the HS MOC to the

SOC within 24 hours of ground receipt. Upon L0 receipt, the SOC performs

packet format checks (e.g., valid headers, checksums). The SOC prepares a

timing product to correct Node clock diﬀerences relative to the Hub timing

and processes IS housekeeping (HK) to calibrated units (L1). L0 data are

provided to the instrument teams for processing, with timing corrections and

L1 HK included as additional inputs. The instrument teams generate and

validate L1 (measurements in engineering units), L2 (science data—magnetic

ﬁeld measurements, particle velocity distributions and the associated moments

and ﬁts— in payload co¨ordinates), and L3 (science data in RTN co¨ordinates)

data products within 30 days of receipt.

L1-L3 data are retrieved by the SOC from the instrument teams within

24 hours of processing and summary plots generated. L4 data products, e.g.

a merger of the MAG and SCM data or combined magnetic ﬁeld and pro-

ton products from across the observatory, are produced at the SOC within 5

working days.

Upon completion of IS commissioning, the SOC begins a period of data

product and instrument performance validation. As data for each orbit are

downlinked, they are routinely and automatically processed. During the subse-

quent orbit, the SDC lead co¨ordinates instrument team validation of the data.

Validation activities proceed through individual calibration and Observatory-

level calibrations. As calibrations are updated, previous orbits’ data are

reprocessed with the updated calibrations, so the process iterates with increas-

ing data volumes of increasing reﬁnement. Validated, calibrated L2 through

L4 data are provided to NASA SPDF for public access upon completion of

the validation period, anticipated to be no more than 5 months, which may

be shortened if reasonable calibrations are available sooner.

Because HS comprises nine spacecraft with slowly changing relative posi-

tions in an equally dynamic plasma environment, specialized tools to assist

researchers in their data selection will be developed and implemented at the

SOC. Many techniques employed by the researchers require speciﬁc Observa-

tory conﬁgurations. To aid the researcher in the selection of processed data,

the SOC is developing interactive queries, but all science data are downlinked

and processed regardless of observatory conﬁguration. As an example, Figure 5

shows a snapshot from a preliminary data selection code using DRM orbit

trajectories.

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6 Analysis Approaches

A variety of multi-spacecraft Analysis Approaches have been previously

developed for missions such as Cluster and MMS. These methods include

calculations of

•

Cascade Rate, measuring of the transfer of turbulent ﬂuctuation energy

from one spatial scale to another [e.g. 177, 178],

•

2-point correlation, measuring the temporal and spatial scale over which

a spectral element is remade by nonlinear processes [e.g. 179, 180],

•

Structure Functions, determining the statistics turbulent ﬁeld increments

to reveal scale-dependent, intermittent turbulence[e.g. 181, 182],

•

Wave telescope, determining the wavevectors of plasma waves and their

associated 3D power distributions[e.g. 183, 184],

•

Pressure-strain interaction, measuring the dilation, −(P ·∇) ·U, which

describes the local conversion between ﬂow and thermal energy[e.g. 185,

186],

•

Curlometer & Gradient Methods, which construct current sheets and

other intermittent structures from spatially distributed measurements[e.g.

125, 187].

Many of these methods and their applications have been documented in ISSI

review articles over the last several decades[76, 77]. In this section, we apply

some analysis approaches to synthetic timeseries constructed using DRM

trajectories corresponding to selected HS conﬁgurations through diﬀerent

numerical simulations of turbulence including two-ﬂuid [188, 189] and hybrid-

PIC [34, 190] nonlinear simulations and quasilinear simulations [191, 192].

We note that due to computational limitations, all the numerical codes used

make approximations in terms of the physical processes included and/or the

scales simulated. Therefore, we do not expect the numerical simulations to be

completely representative of actual plasma turbulence at all scales, and diﬀer-

ences between simulations and HS observations will drive improvements of the

modeling of turbulent transport and dissipation.

6.1 Multipoint Correlations and Structure Functions

Multipoint spectral analysis, 2nd-order structure functions, and space-time

correlation functions yield distributions of turbulent energy in conﬁgura-

tion space [55, 76, 77] and, through time-lagging, decorrelation times for

ﬂuctuations at measured spatial scales [180].

Figure 12 illustrates the temporal and spatial decorrelation of signals

from synthetic magnetic ﬁeld data set constructed by sampling a hybrid-PIC

numerical simulation [34] over trajectories deﬁned by the DRM described in

Section 4.6. The correlation is calculated between all nine trajectories at each

point in the timeseries as

R(|r|, τ ) = ⟨b(x, t) · b(x + r, t + τ)⟩. (4)

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Fig. 12: The spatial-temporal correlation calculated from synthetic HS mea-

surements extracted from a hybrid-PIC simulation of turbulence[34]. By using

all nine trajectories, we are able to resolve the spatial and temporal depen-

dences of Eqn. 4 independently, unlike the auto-correlation from a single

trajectory, presented in the upper right-hand panel, which eﬀectively samples

along the red arrow in the lower left panel, convolving together spatial and

temporal variations.

These correlation values, and how quickly they depart from unity, character-

izes the temporal and spatial scales over which ﬂuctuations are remade by

nonlinear terms, and represents a key statistical property of turbulent dis-

tributions [193] that will be used in G1O1 and G1O2. For comparison, an

example auto-correlation produced using lagged timeseries from a single tra-

jectory (upper right panel) mixes together spatial and temporal dependence.

HS will disentangle spatial and temporal correlations which single SC convolve

together.

The measurement of intense ﬂuctuations at smaller scales while simulta-

neously measuring the distribution of ﬂuctuations at larger scales diﬀeren-

tiates between models of scale-dependent intermittency, testing theoretical

predictions[100, 194–197]. Intermittency also aﬀects diﬀerent types of proton

heating mechanisms in diﬀerent ways, with the associated coherent struc-

tures greatly aﬀect the eﬃciency of certain processes. For example, stochastic

heating occurs when ﬂuctuation amplitudes at the scale of a particle’s gyro-

radius become large [50, 198], which are enhanced near coherent structures.

Conversely, dissipation mechanisms such as Landau damping are less aﬀected

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−1

n = 6

n = 5

n = 4

n = 3

n = 2

n = 1

0.5

1.5

2.5

0 1 2 3 4 5 6

Fig. 13: HS’s multiscale conﬁguration enables the calculation of multiple

orders of structure functions (left panel), that when ﬁt to a power-law S

∝ λ

(center) or recombined into quantities such as kurtosis S

(right) can be

compared to theoretical predictions [e.g. [26, 194, 195]] to characterize the

scale-dependent intermittency in turbulence (G1O4).

by intermittency [123]. HS multiscale measurement of higher order intermit-

tent statistical measures, along with temperature and temperature anisotropy

reveal deep connections between cascade, intermittency and dissipation.

One means of quantifying the intermittency of a system is illustrated in

Figure 13, where we calculate the scale-dependent structure function S

using

synthetic times series drawn from the same hybrid numerical simulation of

turbulence [34]. Instead of using increments drawn from a single timeseries

(λ = τ v

) = ⟨[δz(t + τ ) − δz(t)]

⟩ (5)

[182], increments are calculated using all nine timeseries combined with HS’s

spatial resolution and conﬁgurations and a modiﬁed form of Taylor’s hypoth-

esis [179] allowing for orders of magnitude more samples to be used at a given

scale both along and transverse to the magnetic ﬁeld and ﬂow directions,

(t + τ) − x

(t)] = ⟨{δz[x

(t + τ)] − δz[x

(t)]}

⟩ (6)

enabling the calculation of the higher order structure functions spanning ion

kinetic (blue, left panel), transition (purple), and MHD (red) scales; for N

increments measured, structure functions of order n = log

[N] − 1 can be

resolved [199, 200]; HS enables the study of higher order S

than previous

missions, where diﬀerences between theoretical descriptions are more easily dis-

tinguishable. From these measurements of S

, theories about intermittency as

a function of scale [181], which describe how frequently and how abruptly sharp

structures of diﬀerent sizes and shapes arise, are tested by ﬁtting S

∝ λ

over diﬀerent scale ranges (center); the trending of the ﬁt parameters with

order n is used to validate, falsify, or improve theories [e.g. [26, 194, 195]. Com-

bined with other metrics such as kurtosis (right panel) as well as the analysis

method presented in Figure 14, HS characterizes turbulent intermittency as a

function of scale addressing G1O4.

Fig. 14 illustrates with the same simulated synthetic DRM timeseries used

for Fig. 12 another way in which HS will provide science closure on G1O4 by

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Fig. 14: HS measures intermittency at MHD (red) and sub-ion (blue) scales

simultaneously from diﬀerent numerical simulations, providing science closure

on G1O4 by diﬀerentiating between models of nonlinear coupling that predict

enhanced amplitudes of normalized Elsasser ﬂuctuations δz

⊥

at small scales

(right, from a turbulent hybrid-PIC simulation [34]) compared to a scale-

independent normal distribution of amplitudes (left, drawn from ensemble of

randomly-phased wave modes.).

using its 36 baseline separations to simultaneously quantify the distribution of

turbulent ﬂuctuations at large and small scales. Following Mallet et al 2015[48],

we deﬁne the ﬂuctuation amplitude increment

δz

⊥

= |δz

⊥

| = |z

⊥

+ r

⊥

) − z

⊥

)| (7)

where r

⊥

is the separation in the plane perpendicular to the mean magnetic

ﬁeld direction B

. Using both the synthetic HS timeseries drawn from a hybrid-

PIC simulation, as well as timeseries constructed from a collection of randomly

phased waves, we calculate δz

⊥

as a function of scale λ = |r

⊥

| for an ensemble

of separations. We then calculate the median value of the increment δ

⊥

over

a series of bins spaced logarithmicaly in λ, and normalize the probability dis-

tribution function of the increments in each bin by the median. For the trivial

case of randomly-phased waves, the increments are normally distributed, and

there is no variation as a function of scale. For the case of simulated turbulent,

the intermittency increases with decreasing scale, seen in the transition from

red (large, MHD scales) to blue (smaller, ion-kinetic scales). As the intermit-

tency of a turbulent system depends on the nature of the nonlinear interactions

that transport energy through a system, these types of distributions represent

a sensitive test of diﬀerent models of turbulence.

6.2 Curlometer and Gradient Techniques

Wave telescope and curlometer techniques reveal the nature of ﬂuctuations and

identify structures within turbulence. Gradient estimation is closely related

and is required for determining the pressure-strain tensor and the production

rate of internal energy.

As an example of a novel application of gradient techniques enabled by a

multi-spacecraft observatory, estimates for the spatial gradients from synthetic

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Fig. 15: HS’s SC positions (red points) enable a high-ﬁdelity reconstruction

(perfect measurements shown in blue, measurements with included systematic

errors in green) of the magnetic ﬁeld (arrows) over a larger volume of space,

enabling the simultaneous study of ion-scale structures (e.g., current sheets,

shown as contours at left) with suﬃcient accuracy to address G1O4 (regions of

reconstruction with less than 5% and 10% error shown at right, as explained

in the text).

timeseries drawn from a two-ﬂuid numerical simulation of turbulence[188] are

used in a ﬁrst-order reconstruction to reconstruct a 3D synthetic magnetic

ﬁeld, shown in Figure 15 and described in detail in [201]. By using a weighted

average of the ﬁrst-order estimates for the reconstructed magnetic ﬁeld drawn

from the spatial gradients determined from the 126 unique tetrahedra that

comprise the HS Observatory, we accurately reproduce the magnetic ﬁeld over

large volumes of the simulation. For a selected DRM interval in a good poly-

hedral conﬁguration, we reconstruct the simulated turbulent magnetic ﬁeld

(black/blue arrows indicate the simulated/reconstructed ﬁeld). Averaging over

many spatial locations in the simulation, this analysis method yields ≤ 5% rel-

ative error over a volume of nearly 1.82 ×10

(solid blue line, right panel)

and ≤ 10% error over a volume of 3.208 × 10

(dashed blue line).

To quantify the impact of systematic errors on this analysis technique,

we introduce random oﬀsets replicating estimated systematic errors to each

component of the measured magnetic ﬁeld at all nine SC (green lines). This

produces reconstructed volumes of 3.66×10

(1.77×10

) km

for the 5% (10%)

error thresholds. By leveraging the large number of tetrahedral conﬁgura-

tions sensitive to many length scales simultaneously, HS enables simultaneous

studies of both MHD-scale structure as well as much smaller current sheets,

bringing closure to questions about the transfer of energy from ﬁelds to ﬂows

(G1O3) and associated heating near ion-scale intermittent structures (G1O4).

As discussed at the beginning of this section several other multispacecraft

analysis methods, previously implemented on missions such as MMS and Clus-

ter, can be immediately applied to HS observations, or extended to incorporate

information from all nine spacecraft in the observatory, e.g. [178, 202–205].

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7 Conclusions

Turbulence is the process by which energy contained in ﬂuctuating magnetic

ﬁelds and plasma motion cascades from larger to smaller spatial scales, and

ultimately into thermal energy of charged particles comprising the plasma. In

addition to being a key process that heats cosmic plasmas, it also creates the

conditions in which all universal plasma processes (e.g., magnetic reconnec-

tion, shocks, particle acceleration) act, both within the heliosphere and in all

astrophysical domains. Due to its fundamentally multiscale nature, only spa-

tially distributed, simultaneous measurements provide the data needed to bring

closure to outstanding questions about the distribution and transfer of turbu-

lent energy. HS achieves its mission objectives through an innovative swarm

implementation of high-heritage mission elements, ranging from instruments,

to spacecraft, operations, and analysis tools. HS provides a paradigm shift in

mission design where the many elements of the swarm and the way they inter-

act form an Observatory that is far more than the sum of its parts. As the

ﬁrst multipoint, multiscale mission, HS gives an unprecedented view into the

nature of space plasma turbulence.

Acknowledgements We are deeply indebted to the incredible members

of the HelioSwarm science, engineering, and proposal teams whose tireless

eﬀorts enabled this mission. Construction and analysis of the HelioSwarm

Observatory Design Reference Mission trajectories was supported in part

by the HelioSwarm Project funded under NASA’s Prime contract no.

80ARC021C0001.

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