S9-１
Particle Acceleration in Cosmic Plasmas: Relativistic Surfing Acceleration
宇宙プラズマ中での粒子加速：相対論的波乗り加速
Masahiro HOSHINO
星野真弘
Department of Earth and Planetary Science, Faculty of Science, University of Tokyo,
Hongo, Bunkyo-ku, Tokyo 113-0033, Japan東京大学大学院理学系研究科・地球惑星科学専攻，〒113-0033 東京都文京区本郷
The production of energetic particles is explored for collisionless shocks and magnetic reconnection byusing full particle simulations and analytic study, and it is argued that “surfing acceleration” can provide
the quick and strong energiztion than that believed before. Large amplitude and small scale electrostatic
field, which is a necessary condition for the strong surfing acceleration, can be easily generated in cosmic
plasmas. Therefore, non-adiabatic particles trapped by the potential well of the large amplitude wave arecapable of reaching relativistic energies.

1. Introduction
The origin of high energy particles is along-standing problem in cosmic plasmas. One of
the most widely applied acceleration processes isthe diffusive shock acceleration, and it is wellknown that electric and magnetic field turbulenceacts to scatter the high energy particles in bothshock upstream and downstream, and gain energies
from the converging turbulent waves.
In contrast to this acceleration mechanism underturbulence, the modern satellites observed thecoherent, small-scale, large-amplitude electric fieldwaves embedded in turbulence in many key regionsof terrestrial magnetosphere, and it is now discussed that the coherent waves may be also
responsible to the plasma thermalization andacceleration. The scale of the small-scale wave isof several tens of Debye length, but the amplitudeof the wave is 10 to 100 times that of the motional
electric field induced in the MHD scale. Then it isproposed that the micro-scale processes appear tocontrol the global dynamics.
This kind ofmulti-scale coupling process is beginning to shedlight on not only the space plasma phenomena but
also the high-energy astroplasma physics.
In particularly, the so-called “surfing acceleration” discussed first by Sagdeev and Shapiro [1], is
now believed to be widely applied in many cosmic
plasma settings. The surfing acceleration is one of“direct” acceleration mechanisms, in which theparticles trapped by a small-scale, large amplitude
wave can resonate with the electric field normal to
the wave structure. In this paper, we discuss thatthe surfing acceleration mechanism plays a significant role on relativistic particle acceleration inmagnetosonic shocks and in magnetic reconnection.
2. Surfing Acceleration

In spite of enormous progress in understanding of
surfing acceleration, there still remain fundamental
questions: how the non-thermal acceleration efficiency is controlled by the plasma parameters,
whether or not the energy spectrum is approximatedby a power-law spectrum that is often observed forcosmic ray sources. The maximum energy that thesurfing acceleration can provide is another important question. Effect of plasma turbulence on thesurfing acceleration is probably an important quest
to understand the relationship between the conventional stochastic acceleration and the directacceleration.
The basic mechanism of the surfing acceleration
can be simply described by the balance between theelectric field force (eE) and the Lorentz force
eVxB/c) in the Lorentz equation. Let us assume alarge amplitude electric field (Ex) imposed in thex-direction, the normal, ambient magnetic field(Bz) in the z-direction. Also assume the electricfield (Ey) in the y-direction. In this geometry, if aparticle moving toward the y-direction with thevelocity (Vy) satisfy the force balance condition ofEx + Vy Bz/c = 0, and are trapped by a wave potential well, the particle can gain energy from Ey electric field. If the amplitude of Ex becomes the order of the ambient magnetic field Bz, the particle
can be accelerated up to relativistic energy.
Recently several people discussed that the strong
electric field can be easily excited in many situations such as shock front regions and magnetic
diffusion region of reconnection where the ion inertia effect dominates.
3. Magnetosonic Shocks CaseLet us start from the case of magnetosonicshocks. Among a various high energy particle
acceleration sites in astrophysical plasmas, the moststrong particle acceleration is believed to occur incollisionless shocks. Interplanetary shocks induced by solar flares, supernova shocks, andextragalactic radio sources by jets are those examples. The shock surfing acceleration has been
extensively discussed since 1970’s.
In early
investigation, the shock surfing are studied foracceleration for ions by utilizing the ambipolarelectric field induced by inertia difference between
ions and electrons at the shock front [2], andrelativistic ions may be generated when the Alfven
velocity becomes close to the speed of light.
Since the conventional surfing acceleration utilize the electric field excited at the shock front, it isdiscussed that only ions can be trapped at the shock
front, and electrons are not the case. But recently,
several people discussed that not only ions but also
electrons can be effectively trapped in the shock
front region by large amplitude waves generated by
two-stream instabilities [3]. Also shown that theamplitude of electrostatic field can becomes larger
than the magnetic field when the Alfven Mach
number exceeds several tens, and the electrons areaccelerated into relativistic energies.
In addition to the surfing accelerations in theform of electrostatic potential, Hoshino [4] alsosuggested that the surfing acceleration of particles
trapped by the magnetic potential is possible, andboth positrons and electrons are shown to be surfing-accelerated in relativistic, magnetosonic shocks
by using relativistic particle simulation.
From the above studies, it is now believed thatthe surfing acceleration is very important mechanism for producing high energy particles in a various different shock situations.
4. Magnetic Reconnection Case
Next we will show that magnetic reconnection
also involve the surfing acceleration for generationof non-thermal particles. Many plasma states inuniverse have magnetic fields whose structure contains the neutral sheet where the magnetic fieldpolarity changes its direction, and magnetic
reconnection also plays a crucial role on the magnetic energy release and the resultant plasma heating/acceleration. Reconnection is believed to beparticularly important in celestial magnetospheres
such as terrestrial magnetosphere, solar atmosphere,
pulsar magnetosphere, and accretion disks in X-ray
binaries and active galactic nuclei etc.
The energization of charged particles inreconnection is basically provided by the interaction of the charged particles with an electric fieldaround the X-type region. In the earliest exploration of particle acceleration during reconnection,

the test particle calculations based on the magnetic
and electric fields structure obtained by the resistive
MHD model demonstrated the production of supra-thermal particles by moving in the direction of
the electric field over a substantial distance.
Hoshino et al. [5] noted that large amplitude turbulence can be generated in collisionless reconnection,
because the plasma sheet becomes as thin as ion
inertia scale, and because kinetic instabilities suchas beam instabilities are easily switched-on. They
explored electron acceleration by using full particle
simulations and showed that electrons accelerated
around the X-type region are further accelerated
under electromagnetic turbulent fields around themagnetic field pile-up region formed by thereconnection jets.
In addition to the above acceleration, Drake et al.
[6] also demonstrated that large amplitude, bipolarelectric field can be generated in and around theX-type region, and found that the electrostatic fields
parallel to the magnetic fields plays an importantrole on acceleration. During this nonlinear stage,
Hoshino [7] found that the ambipolar electric fieldnormal to the magnetic field can be excited aroundthe X-type region, and the electric field grows up toalmost same amplitude as the local magnetic field.
Therefore, the shock surfing can be switched-on
around the X-type region, and high energy particles
are generated in reconnection.
We have only begun to investigate the potentiallyrich multi-scale structuring phenomena that result
from the coupling of the MHD scale to the scale ofelectron kinetics. Further studies should help toelucidate how particle acceleration are provided incosmic plasmas.

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[4] M. Hoshino, Prog. Theor. Phys. Suppl. 143 (2001)
149.
[5] M. Hoshino, T. Mukai, T. Terasawa, and I.
Shinohara, J. Geophys. Res. 106 (2001) 25979.
[6] J. F. Drake et al., Science 299 (2003) 873.
[7] M. Hoshino, to be published in Geophys. Res. Lett.
(2004)