QED cascade induced by a high-energy $\gamma$ photon in a strong laser field

The QED cascade induced by the two counterpropagating lasers is studied. It is demonstrated that the probability of a seed photon to create a pair is much larger than that of a seed electron. By analyzing the dynamic characteristics of the electron and positron created by the seed photon, it is found that the created particles are more likely to emit photons than the seed electron. With these results, furthermore, we demonstrate that the QED cascade can be more easily triggered by the seed photon than by the seed electron with the same incident energy and the same laser.

Figure 1

Comparison between the radiation spectrum (red line) and the energy distribution of the emitted photons (column diagram). The area below the radiation spectrum has been normalized.

Figure 2

The probability of a seed photon to create a pair with $I=5\times {10}^{24}\mathrm{W}/{\mathrm{cm}}^2$. The incident energy is, from top to bottom, $\varepsilon =600$ (black line), 400 (red line), 200 (green line), and 100 (blue line). At $t=-7.5$, the photon encounters the leftward laser, then the photon has the probability to create a pair. At $t=2.5$, the photon passes through the laser.

Figure 3

The probability to create a pair by different seeds with different incident energy and different laser intensity. The dashed lines show the probability of a seed photon. The open circle line indicates the statistic probability of electrons for a large number (${10}^5$) and the solid lines are the polynomial fitting. In (a), the intensities of the laser, from left to right, are $I=2\times {10}^{25}$ (black), $I=1\times {10}^{25}$ (red), $I=8\times {10}^{24}$ (green), and $I=5\times {10}^{24}\mathrm{W}/{\mathrm{cm}}^2$ (blue). In (b), the incident energy of the seeds is 1000 (the left black lines) and 200(the right red lines), and the intensity is scaled to match $I_0={10}^{23}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 4

The probability for emission of the (a) electrons and (b) positrons created by the seed photons $\varepsilon =400$ and that of the seed electrons (c) $\gamma =400$ in the laser $I=5\times {10}^{24}\mathrm{W}/{\mathrm{cm}}^2$. Because of randomness, the pairs are created at a different time and the probability of the different sample is different.

Figure 5

The dynamic characteristics of the pair created by a seed photon $\varepsilon =400$ [(a) created electron and (b) created positron] and that of a seed electron (c) $\gamma =400$ with $I=5\times {10}^{24}\mathrm{W}/{\mathrm{cm}}^2$. The pair is created at $z=9.026$ and $t=-5.97$ and the initial energy of the created electron is (a) ${\gamma }_{e0}=338$ and the energy of the positron is (b) ${\gamma }_{p0}=62$; thus, we can have energy conservation as ${\gamma }_{e0}+{\gamma }_{p0}=\varepsilon$.

Figure 6

The number of the created pairs $N^{\mathrm{pair}}$ in the cascade, from top to bottom, induced by the 1000 seed photons with incident energy $\varepsilon =600$ (black line), $\varepsilon =400$ (red line), $\varepsilon =200$ (blue line), and the 1000 seed electrons with incident energy $\gamma =600$ (pink line), $\gamma =400$ (green line), and the intensity of the laser is $I=5\times {10}^{24}\mathrm{W}/{\mathrm{cm}}^2$. At time $t=0$, the number of created pairs is $1320,1080,832$ for the seed photons and $347,54$ for the seed electrons.

Figure 7

The average number of the created pairs $N_a$ in the cascade induced by a charged particle in the laser $I=5\times {10}^{24}\mathrm{W}/{\mathrm{cm}}^2$. To ensure the linear relationship, we just match the values in Fig. 6 in the interval between time $t=7$ and $t=13$. Before or after this interval, the linear property would be lost as the overlap region of the two lasers becomes smaller and smaller.

Figure 8

The creation probability of seed electrons with different incident energy and different laser intensity. The open circles indicate the creation probability using the Gaussian pulse as shown in Fig. 3 and the solid circles represent the results of the cylindrical pulse. The statistical number is ${10}^5$, and the intensities of the pulses are, from left to right, $I_0=2\times {10}^{25}$ (black line), $I_0=1\times {10}^{25}$ (red line), $I_0=8\times {10}^{24}$ (green line), and $I_0=5\times {10}^{24}\mathrm{W}/{\mathrm{cm}}^2$ (blue line).