7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Compressible MHD Turbulence and Cosmic Ray TransportHuirong Yan121
Deutsches Elektronen Synchrotron DESY, 2 Institut für Physik und Astronomie, Universität
Potsdame-mail (speaker): huirong.yan@desy.de

The interstellar medium is turbulent on scales ranging
from AUs to kpc (Armstrong et al. 1995). Both the spectraof CRs and the ISM turbulence show big power laws,
suggesting a strong interrelation of the two.
A new chapter of CR propagation research has begun
when studies of particle transport and interstellar
turbulence can confront each other. Our recent analysis ofMagnetospheric Multiscale (MMS) MMS data confirms
the scale dependent anisotropy of Alfvenic turbulence(Zhao et al. 2022, Fig.1), which makes it completely
ineffective for scattering particles (Goldreich & Sridhar
1995, Yan & Lazarian 2002). As proposed by our earlier
work (Yan & Lazarian 2004, 2008, henceforth YL04,YL08), the solution rests on thorough understanding ofcompressible turbulence from both theoretical studies andfirst-hand knowledge of turbulence in space.

two bars, the left and right ones represent the percentages ofkinetic and magnetic energies, respectively. b) Fast-mode energy
fractions in the total energy of compressible modes analyzed
from Cluster observations of magnetosheath.

With the advanced techniques we developed for radio
polarization data, it is found that Alfven and compressiblemodes are distinguishable from observations (Malik2023). On small scales, compressible turbulence is muchinfluenced by damping. demonstrated a strong
propagation angle dependence in collisionless and viscousdamping, influencing the three-dimensional (3D) energy
distributions (YL04, YL08). Based on an improved
compressible MHD decomposition algorithm, ourobservational analysis demonstrates that collisionlessdamping enhances the anisotropy of compressible MHD
modes due to their strong pitch angle dependence,
consistent with theoretical expectations (Zhao et al. 2023,Fig. 2b)
Different regimes of particle transport, e.g., diffusion vs.
superdiffusion, isotropic vs. anisotropic diffusion, will be7
discussed in relation to turbulence
properties (see Fig.3).

Fig.1 Analysis of MMS turbulence data at 1Au. a) The variationof !∥ versus !" for magnetic power of "!#$%&'( fluctuations.
b) The ratio *+(-" ) to *+(-∥ ) of fluctuations within -+/+# plane.
*+(-" ) and *+(-∥ ) represent Figure
the 7. normalized
perpendicularThis Fig shows the result when CR with> L and< L interact with large scale eddies inside MHD turbulencewavenumber spectrum, and parallelwavenumber spectrum.
of M 0.73. The results are obtained for Alfvén and mixed modes.
mf pmf p

AThe y axis represents the mean square distance < (d d0)2 >travelled by CR normalised by the box length, L2box . The x axis
represents time,t normalised by the gyrofrequency,⌦. The paralleland perpendicular distances obtained from numerical simulations
are represented by continuous and broken line respectively. Transport are compared here for mf p > L, (dashed and continuouslines) and mf p > L (dotted and dashed dotted lines). Transport iscompared for Alfvén (red plots) and mixed modes(blue plots) here.
The data points are fitted with a line having a slope 1 and particleshas shown normal-diffusion. After introducing artificial scattering,
the transport becomes more isotropic compared to no artificial scattering.

Plasma turbulence is primarily shaped by the forcing onlarge scales and damping on small scales. The multiphasenature of ISM and diversity of driving mechanisms giverise to spatial variation of turbulence properties. We findthat the proportion of magnetosonic modes increases withincreasing compressive forcing
fromturbulence
these two methods. Inthe global frameof reference the magfield is considered to be along the direction of the meansimulations (Makwana & Yannetic2020,Fig.2a).
magnetic field in turbulence. In the local frame of reference
the magnetic field along the particle trajectory is considered.
The particle position, velocity and the magnetic field at
the corresponding position are recorded at each time instancefrom test particle simulations. Particles are initially arranged
in beams. All possible combinations of pairs of particles
within the beam are considered as they evolve with time. For
each pair of particle the separation between them is calculated. The values of the perpendicular distance is obtained byaveraging over all combinations of pairs of particles within
individual beams and then over all the beams.
The results of simulations of particle transport in two different types of turbulence data cubes with solenoidal driving
and a range of different MA are presented here.
TURBULENCE DATA CUBES Type I
These MHD turbulence data cubes are solenoidally driven
and consists of a mix of all MHD modes. The mixed mode
has not been decomposed into MHD eigen modes. Turbu-Fig.2 a) The time-averaged fractions of mode energies indifferent modes in different simulations. Each simulation hasFig.3 a) Cross field diffusion vs. MA. b) Diffusion index vs. theratio of particles’ mean free path and turbulence coherence
scale (Maiti et al. 2022).

Figure 8. This Fig shows the result when CR with mf p < Linteract with large scale eddies in MHD turbulence of various Mach
number, MA . The results are obtained for Alfvén and mixed modes.
?
The y axis represents the ratio of spatial diffusion coefficients, D
Dkof CR and the x axis represents MA of MHD turbulence. The blue
dots represents the diffusion coefficients obtained from simulations
for mixed modes and is fitted with blue dashed line with a slopeof 3.41. The red dots represents the diffusion coefficients obtained
from simulations for Alfvén modes and is fitted with red dashed linewith a slope of 3.5. The fits are closer to the description given byEqn 7.

References[1] Siqi Zhao, H. Yan, T. Z. Liu, et al. 2022, ApJ, 937,
102of various Mach numbers ranging from subAlfvénic tolence
superAlfvénic are studied here for particle transport.
[2]
P. Goldreich, A. Sridhar, 1995, ApJ, 438, 763(We consider the total MHD turbulence data cubes with theAlfvénicMach numberranging...)[3]
SiqiZhao,H.fromYan,
T. Z. Liu, et al. 2023, under
While some earlier particle transport analysis were carried
out
only in the global
frame 2305.12507
of reference,(Xu & Yan 2013)
review;
arxiv:
the current studies are extended to consider the particle transport
in the localof reference as well.
The PRL, 937, 102[4]analysis
H. Yan,A.frameLazarian,2002,
slopes obtained from super diffusion of particles in different[5]numbers
H. Yan,A.inLazarian,
2004,
Mach
are presented
Table 3 The particles
undergo ApJ, 937, 102
super diffusion with the fitting power law index ⇠ 1.5.
[6]
H.inYan,
2008,
The data
the aboveA.
tableLazarianshows that a slopeof 1.5 is ApJ, 937, 102
not observed in the current calculations in the global frame[7] K. Makwana & H. Yan 2020, PRX, 10, 031021
of reference. Instead a slope closer to 1.5 is observed in thelocal frame of reference. The super diffusion of CR in MHD[8] S. Malik, KH Yuen, H. Yan 2023, under review,
turbulence data cubes with different Mach numbers is presented
in Fig. 9 .
arXiv:2303.17282
TURBULENCE DATA CUBES Type II[9] S. Maiti, K. Makwana, H. Zhang, H. Yan 2022, ApJ.,
These MHD turbulent data cubes are generated from the926, codes
94 which are solenoidally driven. The 3D turPENCIL
bulence are decomposed into individual modes and particle
propagation in individual modes are investigated.
The Mach numbers vary from sub Alfvénic to superAlfvénic.