Lorentz-Abraham-Dirac versus Landau-Lifshitz radiation friction force in the ultrarelativistic electron interaction with electromagnetic wave (exact solutions)

When the parameters of electron-extreme power laser interaction enter the regime of dominated radiation reaction, the electron dynamics changes qualitatively. The adequate theoretical description of this regime becomes crucially important with the use of the radiation friction force either in the Lorentz-Abraham-Dirac form, which possesses unphysical runaway solutions, or in the Landau-Lifshitz form, which is a perturbation valid for relatively low electromagnetic wave amplitude. The goal of the present paper is to find the limits of the Landau-Lifshitz radiation force applicability in terms of the electromagnetic wave amplitude and frequency. For this, a class of the exact solutions to the nonlinear problems of charged particle motion in the time-varying electromagnetic field is used.

Figure 1

Electron moving in the rotating electric field emits EM radiation. Due to this the angle between the electron momentum and electric field, $\varphi$, is not equal to $\pi /2$.

Figure 2

(a) Dependence of the components of the electron momentum perpendicular $p_{\perp }$ and parallel $p_{\left|\right|}$ to the electric field [normalized by $m_{e}c{(a_m/{\varepsilon }_{\text{rad}})}^{1/4}$] on the normalized EM field amplitude $a{\varepsilon }_{\text{rad}}^{1/3}$, and (b) dependence of $\varphi$ and electron $\gamma$-factor, normalized by ${(a_m/{\varepsilon }_{\text{rad}})}^{1/4}$, on $a{\varepsilon }_{\text{rad}}^{1/3}$ for $a_m=2500$ and ${\varepsilon }_{\text{rad}}={10}^{-8}$.

Figure 3

Solution of the electron equation of motion with the radiation friction force in the LAD form in the case of the superposition of rotating and radial electric fields. (a) Normalized electron energy $K=(\gamma -1)/({\gamma }_m-1)$ and the angle $\varphi$ vs the electric field amplitude $a/a_m$ with $a_m=2500$. (b) Normalized electron energy $K=(\gamma -1)/({\gamma }_m-1)$ and the angle $\varphi$ vs parameter $d/a$ for $a=50$. Here ${\gamma }_m={[1+{(p_m/m_{e}c)}^2]}^{1/2}$ with $p_m/m_{e}c=700$, $d=250$, and ${\varepsilon }_{\text{rad}}={10}^{-8}$.

Figure 4

Solution of the electron equation of motion with the radiation friction force in the L-L form in the case of rotating homogeneous electric field: (a) Dependence of the components of the electron momentum [normalized by $m_{e}c{(a_m/{\varepsilon }_{\text{rad}})}^{1/4}$] perpendicular $p_{\perp }$ and parallel $p_{\left|\right|}$ to the electric field on the normalized EM field amplitude $a{\varepsilon }_{\text{rad}}$, and (b) dependence of $\varphi$ and the electron $\gamma$-factor [divided by ${(a_m/{\varepsilon }_{\text{rad}})}^{1/4}$], on $a{\varepsilon }_{\text{rad}}$ for $a_m=1500$ and ${\varepsilon }_{\text{rad}}=7.5\times {10}^{-4}$.

Figure 5

Solution of the electron equation of motion in a rotating homogeneous electric field for $a_m=1500$ and ${\varepsilon }_{\text{rad}}=7.5\times {10}^{-4}$. Dependences of the electron $\gamma$-factors on the electric field: ${\gamma }_{\mathrm{LAD}}$ and ${\gamma }_{\mathit{LL}}$ correspond to the radiation friction force taken in the LAD and L-L form, respectively. The normalization is the same as in Fig. 4.

Figure 6

Normalized momentum components $p_{\left|\right|}/m_{e}c={\tilde{u}}_2$ and $p_{\perp }/m_{e}c={\tilde{u}}_3$ vs the rotating field amplitude $a$ and parameter ${\varepsilon }_0$.