Depletion of Intense Fields

The interaction of charged particles and photons with intense electromagnetic fields gives rise to multiphoton Compton and Breit-Wheeler processes. These are usually described in the framework of the external field approximation, where the electromagnetic field is assumed to have infinite energy. However, the multiphoton nature of these processes implies the absorption of a significant number of photons, which scales as the external field amplitude cubed. As a result, the interaction of a highly charged electron bunch with an intense laser pulse can lead to significant depletion of the laser pulse energy, thus rendering the external field approximation invalid. We provide relevant estimates for this depletion and find it to become important in the interaction between fields of amplitude $a_0\sim 10^3$ and electron bunches with charges of the order of 10 nC.

Figure 1

The number $N_T$ of radiating electrons required to see significant depletion plotted as a function of ${\gamma }_e$ and $a_0$. Black curves indicate the depletion thresholds $a_0({\gamma }_e)$ when $N_T=10^9$, $10^{10}$, and $10^{11}$. The dashed white curves represent ${\omega }^{\prime }\mathrm{\Delta }x=\text{const}\gg 1$, so that photon emission is incoherent across the relevant parameter space. Left, using (4). Right, using (6) below.

Figure 2

The dependence of the average number $⟨s{⟩}_e$ of absorbed laser photons on the dimensionless amplitude $a_0$ of the EM field for different values of ${\gamma }_e$. The corresponding distributions $sd{P}^e/ds$ for $a_0=200$ are shown in the inset (b). Black dotted curves represent the numerical fit provided.

Figure 3

The distribution $sd{P}^e/ds$ as a function of $k_{\perp }^{\prime }$ and $k_z^{\prime }$ for ${\gamma }_e=2000$, and for $a_0=200$ (left) and 2000 (right). The distributions are supported on a line $k_{\perp }^{\prime }/k_z^{\prime }=1/10$ and $4/3$ in the left and right panels, respectively, cf. (10). Full curves on the floor represent the ellipses (9) for different values of $s$.