25E09
Spatial Profile of the Energetic Particles in the Upstream of Collisionless Shock
衝撃波上流域での粒子拡散現象
Tooru Sugiyama
杉山 徹
Japan Agency for Marine-Earth Science and Technology3173-25 Showa-machi, Kanazawa-ku, Yokohama 236-0001, Japan（独）海洋研究開発機構 〒236-0001 横浜市金沢区昭和町 3173-25
We have studied the transport properties of energetic particles in the upstream region of parallel shocks
considering the possibility of anomalous diffusion where the density decay profile has not an exponential
profile but a power-law behavior. The results obtained from the hybrid simulation model show that thespatial profiles of the energetic ions are well fitted by a power law distribution. This implies that particle
propagation can be described by a super-diffusion profile even though the power of the magnetic wave issufficient large to scatter the particles.

1. General
Non-thermal energetic particles accelerated
around collisionless shock waves have been
deeply investigated and the main mechanism forthis acceleration is now widely accepted as thestandard diffusive shock acceleration (DSA)
theory (e.g. [1]). The DSA model, based on thediffusion-convection equation, predicts that theobtained energy spectrum exhibits a power-law
shape and that the spatial distribution of theparticle density, especially in the upstream,decays exponentially with distance from theshock surface.
Recently, another explanation has been
proposed, according to which the diffusion
profiles are different from the normal Gaussian
diffusion described by an exponential function as
noted above. Perri & Zimbardo ([2-4]) havereported that the upstream density profiles of theenergetic particles associated with the reverse
shock of the corotational interaction region (CIR)
and termination (TA) shock are not described by
the normal Gaussian diffusion. They discussed
the diffusion profiles with regard to the intensityof the magnetic field turbulence for particle
scattering. Since a weak turbulence reduces thescattering efficiency, the super-diffusive profile isobserved in the region with weak turbulence.
Sugiyama & Shiota ([5,6]) have reported that theupstream density profiles of the CME-driven
interplanetary shock (IP shock) are not describedby the normal Gaussian diffusion. The essential
differences in the particle dynamics between CIR,TA, and IP shocks are the wave-particle
interaction processes. In the upstream of the IPshock, the amplitude of the magnetic field is
sufficiently larger than that discussed around CIR

and TA shocks. Non-linear wave-particle
interaction processes should be considered as
discussed in their paper, especially, with the pointof no long trend of the spatial profile of theupstream wave amplitude. Here, we have reported
the transport profiles of the shock-accelerated
ions using a Hybrid numerical simulation. Theresults show that the motions of the accelerated
particles seem not to be the normal Brownian
motion.
2. Simulation Model
The Hybrid model used in this study treats theions as macro-particles while the electrons aretreated as a charge-neutralizing massless fluid. The
simulations are one-dimensional in space (shocknormal direction in X: positive X directsdownstream) but fully three-dimensional in velocity.
Initial magnetic field lies on X axis pointing todownstream region. All particles are referred as
proton. Time, and length are normalized by the
inverse of proton gyro-frequency ci, and the ion
inertia length i, respectively, based on theupstream parameters. A shock wave is set up by theconventional way (conductive wall method). The
simulations are performed in the downstream-rest,normal-incident frame. Initially, there are noupstream turbulence in field and no seed particles in
the upstream region, that is, a quiet-start model isused. The shock Mach Number MA and shock angle
are 9.6 and 0 degree. The grid-cell size and the time
step size are 0.5 and 0.002, respectively, in thenormalized unit. The simulation system length is320,000 i, long. Initially 500 particles per grid-cellare used for the unit density in the incoming
thermal distribution. Because of this large systemsize and large number of particles compared withthe previous runs, we can clearly follow the spatial
and temporal feature of the energetic component
with statistically reliable number of particles.
3. Results
Figure shows a particle orbit from the one of theaccelerated particles in time and position plane.
Shock is located at X=0, and negative values in X
axis means that particle locates in the upstream
region. Some characteristic profiles are observed;
RUN and STAY time intervals, which clearlyindicate the trajectory is far from the normal
Brownian motion, but like Lévy flight. This leads
the motion of the particles are not described by thenormal Gaussian diffusion, but the non-classicaldiffusion of the super-diffusion. Details about thespatial profiles of the density of the accelerated
particles and the wave power are discussed inpresentation.

3000

Time [ 1/ci ]

2500
2000
1500

1000-60000 -50000 -40000 -30000 -20000 -10000
Position [ i ]Fig.1. An orbit from one of the accelerated particles.
RUN (T=~1400~1800) and STAY (T=~1200~1300,~1800~2400) are observed.

Acknowledgments
The simulations are performed on the Earth
Simulator on the project of “Space and Earth
System Modeling”.
References[1] R. D. Blandford and J. P. Ostriker: ApJ, 221 (1978)
L29.
[2] S. Perri and G. Zimbardo: ApJ, 671 (2007) L177.
[3] S. Perri and G. Zimbardo: J. Geophys. Res. 113(2008) A03107.
[4] S. Perri and G. Zimbardo: ApJ, 693 (2009) L118.
[5] T. Sugiyama and D. Shiota: ApJL. 731 (2011a) L34.
[6] T. Sugiyama and D. Shiota: AIP Conf. Pro. (2011b)
in press.