Non-thermal heating of plasma particles
due to relativistic nonlinearity of lasers= Modeling cosmic-ray acceleration in laboratory =Hideaki Takabe, NTU, Taiwan
1.

Laser acceleration by wake-field induced by ponderomotive force2.

An experiment shows no mono but power-law heating (Pinch to Chance)

3.

Stochasticity of the particle motion by filamentation and reflection of laser

4.

Power law spectrum by nonlocal diffusion in p-space. (FFPE)

5.

Generation of waves and cosmic-rays in relativistic collisionless shocks in Universe

6.

Proposal to NIFS
核融合科学研究所ユニット構築会議への提案として用意した。ZOOM会議。2021年7月5日
Main reference: HT book-1; https://www.springer.com/gp/book/9783030496128

1Laser wake-field acceleration

2𝜋𝑐𝜔[GV/m]
Force[MV/m]
HT book-1 p. 206
Electrons in 2-D 3-D

3km
XFEL, DESY, Hamburg (17GeV/1.7km)

2

LFEX experiment at ILE

蔵満（阪大）

ChancePinch

Y. Kuramitsu, Model Experiment of Cosmic Ray Acceleration due toan Incoherent Wakefield Induced by an Intensive Laser Pulse”,
Physics of Plasmas (Letter), 18, 010201 (4 pages), (2011),
Y. Kuramitsu et al, NONTHERMAL ACCELERATION OF CHARGED PARTICLES DUE TO AN
INCOHERENT WAKEFIELD INDUCED BY A LARGE-AMPLITUDE LIGHT PULSE, The Astrophysical3Journal, 682: L113 (2008)

Cosmic-rays and observation fact

Rel. Shocks

Extra-G
GalaxySun

Non-R. Shocks

Artistic view of the avalanche of created many particle inthe air triggered by an injection of one high-energy
cosmic-ray to the air. Molecules in the air decays shortlife particles to create also another particles like chain
reaction.
D. Castelvecchi, Nature 549, 440 (2017).

T. Gaisser, arXiv:1704.00788v1, astro-ph.HE (2017)4

Standard model of accelerating cosmicrays (DSA)=Non-relativistic shocks=
40 years old

E. Fermi, Astrophys. J. 119, 1 (1954).
A. R. Bell, Mon. Not. R. Astro. Soc. 182, 147 (1978).
R. D. Blandford & J. P. Ostriker, Astrophysical J., 221, L29 (1978)

A. R. Bell
Tokyo I T, Feb. 22, 2007

Power law for non-thermal particles
Collisionless shockdN(E) E dEE n  E 0 (1  ) nN(E)  N 0 (1  P)n  1  ln(1  P) / ln(1  )  1  P /   E / E  1 P /   1Relativistic shocks?

3R 1N(E) ~ E-2 for R=45

X-ray image of SN1006 and DSA
１．Relativistic Synchrotron Emission

SN1006
u0= 4330km/s
diameter = 60 ly

２．Shock Thickness (Observation)

WX = 1×1017 cm (=1/400 lmfp)

WX

G. Casssam-Chenai et al., Astrophys. J. 680, 1180 (2008)
A. Bamba et al., Astrophys. J. 621, 793 (2005).

Chandra Xray6SatelliteWe have demonstrated non-relativistic collisionlessshock formation in experiment with NIF laser
John Dawson Award for Excellence in Plasma Physics Research
American Physical Society, 2020 Awardee
https://www.aps.org/programs/honors/prizes/dawson.cfm
Nonlinear Physics of Magnetic Turbulence, Shock Formation, and Particle
Acceleration via Weibel Instability in Laser Astrophysics= Theory, PIC Simulation and Laser Experiment =Presented at Prof. Yoshida’s final seminar, March 7-8, 2021 by ZOOM
(Video of my talk)

http://www.ppl.k.u-tokyo.ac.jp/takabe.mp4

Next is relativistic shocks and cosmic-ray acceleration physics
7

Global Structure of 2D ionPrevious one-dimensional (1D) particle-incell (PIC) simulations showed thatsynchrotron maser instability (SMI) is thesignificant dissipation mechanism for
relativistic magnetized shocks (e.g.,Langdon et al. 1988; Gallant et al. 1992;
Hoshino et al. 1992; Amato & Arons 2006).

M. Iwamoto et al., Precursor Wave Amplification by
Ion–Electron Coupling through Wakefield in
Relativistic Shocks, The Astrophysical Journal Letters,
883:L35, (2019).

relativistic shocks

Relativistic EM waves (Lasers)= Relativistic shocks =∥ +=Strength parameter
Lorentz invariant
HT book-1, Chapter59

An electron motion in relativistic laser (Nonlinear)
dp x
  ev y B z  eE xdt

dpydt
mc 2

 eEy  evxBzd  ev y E y  ev x E xdt

AtABz 
zEy  A  A0 cos      t  x / c  0

dp x
a  ydt
x

dpyda

dt
dtd
a
 ydttpy  a 1 2 1  2px py 22px HT book-1 p. 287
10

Solution of anelectron motion

acceleration phase

Incident laserNon-linear oscillation

Figure of 8 motion

11Motion is chaotic due to reflected laser andfilamentation

S. Rassou, A. Bourdier, and M. Drouin, Phys. Plasmas 21, 083101(2014)

HT book-1, Chapter 912

Levy’s nonlocal transport (FFPE) canexplain the non-thermal components

ChancePinch

C. Tsallis et al., Phys. Rev.
Lett. 75, 3589 (1995)

HT book-1, Chapter 9J. Anderson et al., Phys. Plasmas 21, 122109 (2014)

13

LFEX experiment (ILE) can be explained bychaotic heating with relativistic intensity lasersS. Kojima, et al. Electromagnetic field growth triggering super-ponderomotive electron acceleration
during multi-picosecond laser-plasma interaction. Commun Phys 2, 99 (2019).

HT book-1, p. 353
14

EM waves induced by collisionless shocks in Space
Figure 1. Shock structure for σe = 5 atωpet = 2000. The out-of-plane magnetic
field Bz, the 1D profile of Bz, thelongitudinal electric field Ex, the yaveraged electric field Ex, and the phasespace plots in the x–uxs plane forelectrons and ions are shown.

M. Iwamoto et al., Precursor Wave Amplification by Ion–Electron Coupling throughWakefield in Relativistic Shocks, The Astrophysical Journal Letters, 883:L35, (2019).

HT book-1, p. 354
15

Proposal to the NIFS unit
• Study the theory of chaotic acceleration of electrons byrelativistic EM waves• Relate the theory to the physical mechanism of cosmic-ray
acceleration in relativistic regime (E > 1015 eV)• Carry out big computing to visualize the physical mechanism• Design a verification experiment with reasonable facility
parameters• Perform the experiment with any of international facilities like
ELIs in EU.
• Challenge to propose a new theoretical mode and experimental
proof to the big community of the cosmic-ray research.
16