28E43P
超相対論レーザー電子相互作用における量子効果を含む放射の反作用モデル
Radiation Reaction with Quantum Effects
in Ultrarelativistic Laser Electron Interactions
瀬戸慧大1、長友英夫1、甲賀ジェームス2、三間圀興1
Keita SETO1, Hideo NAGATOMO1, James KOGA2 and Kunioki MIMA1
1

大阪大学レーザー研、2原研関西研
1
ILE, Osaka Univ. , 2Kansai Inst., JAEA
With the rapid progress of the ultra-short pulse laser
technologies, the maximum intensities of these lasers havereached the order of 1022W/cm2 [1, 2]. One laser facility
which can achieve such ultra-high intensity is LFEX
(Laser for fast ignition experiment) at Institute of Laser
Engineering (ILE), Osaka University [3] and another isthe next laser generation project, the Extreme Light
Infrastructure (ELI) project [4] in Europe. If an electron isin the strong fields caused by a laser which intensity islarger than 1018W/cm2, the dynamics of the electron
should be described by relativistic equations. The mostimportant phenomenon in this regime is the effect of theponderomotive force, where an electron is pushed in thepropagation direction of laser. When a charged particle isaccelerated, it proceeds in a trajectory accompanied withbremsstrahlung. If the laser intensity is higher than1022W/cm2, strong bremsstrahlung might occur.
Accompanying this, the “radiation reaction force (ordamping force)” works on the charged particle. Therefore,
it is necessary to study the radiation reaction effects in theultra relativistic laser-electron interaction regime. We canconsider this effect as a “self-interaction”. In the laser
electron-interaction at this intensity level, one of theimportant equations is the equation of motion with thereaction force. This field is based on H. A. Lorentz’s work[5]. The purpose of his study was research of the electron’scharacteristics via classical physics. After this work, P. A.
Dirac updated Lorentz’s theory with the relativistic
covariant equation of motion, as the LorentzAbraham-Dirac (LAD) equation in Minkowski spacetime[6]. Dirac suggested the covariant form of the radiation
reaction force should be described with, not only theretarded potential, but the advanced potential. This method
resulted in an equation on which covariance is. The
starting point of discussion is this LAD equation asfollows.
dw µ(1)m0 = Fex µ + f reaction µdτ
d 2 w µ m0τ 0  dw dw  µ(2)=+ 2 gf reaction µ m0τ 0,w
dτ 2c dτ dτ Where τ 0 = e 2 6πε 0 m0 c 3 , w, τ and g is therelativistic 4-velocity, proper time and Lorentz metric.
This equation is named the Lorentz- Abraham-Dirac(LAD) equation, which has the run-away (infinite value)
solution. It is assumed to be pre-renormalization (notrenormalized equation). When we solved Eq.(1), we needto treat as something trick like the renormalization in thequantum electrodynamics (QED).
However, an electron is a basic particle which has
the charge, the mass and the spin 1/2. The property of thespin, in particular, is important in the quantum dynamics,
but the normal theory of relativistic doesn't contain it. In
QED, the spin is used like the label which distinguishes
physical state. The Dirac equation is the electronequation which has the spin information [7].
 µ
ie (3)0iγ  ∂ µ −  Aµ  − mc  ψ =
The equation (3) contains electron-electromagnetic fieldinteractions. But, this equation cannot back to therelativistic0 ,(m w ) (m w ) − m c =relation as0µµ02 20becomes0.
(4)( m w ) ( m w ) − m c − 2e σ F =0µµ02 20µνµν

The Dirac equation of Eq.(3) has additional term of− e 2 × σ µν Fµν [8]. This term means the interaction of
spin-electromagnetic field. Dirac considered this LAD
theory for the classical theory of the electron. Therefore,
the spin didn't treat in this classic theory. Therefore, theradiation reaction with spin dipole momentum should be
prepared for the ultrarelativistic laser-high γ electroninteractions. We will discuss about how to treat the spinin the radiation reaction via the Stern-Gerlach's spin
theory.
[1]
V. Yanovsky, V. Chvykov, et al., Opt. Express 16, 2109
(2008).
[2]
G.A.Mourou, C.P.J.Barry and M.D.Perry, Phys. Today
51,22 (1998)[3]
N. Miyanaga, H. Azechi, K. A. Tanaka, et al., “FIREX
Petawatt Laser Development for Fast Ignition Research at ILE,Osaka”, Proc. of IFSA 2003 (American Nuclear Society Inc. )pp507-511 (2004).
[4]
Report on the Grand Challenges Meeting, 27-28 April
2009, Paris[5]
H. A. Lorentz, The Theory of Electrons and Its
Applications to the Phenomena of Light and Radiant Heat, A
Course of Lectures Deliverd in Columbia Univ., New York, inMarch and April 1906, 2nd edition (Leipzig, New York, 1916)[6]
P. A. M. Dirac, Proc. Roy Soc. A 167, 148 (1938).
[7]
P. A. M. Dirac, Proc. Roy Soc. A 117, 610 (1928).
[8]
J. W. Holten, Nuclear Physics B356, 3 (1991).