Physical Mechanism of the Transverse Instability in Radiation Pressure Ion Acceleration

The transverse stability of the target is crucial for obtaining high quality ion beams using the laser radiation pressure acceleration (RPA) mechanism. In this Letter, a theoretical model and supporting two-dimensional (2D) particle-in-cell (PIC) simulations are presented to clarify the physical mechanism of the transverse instability observed in the RPA process. It is shown that the density ripples of the target foil are mainly induced by the coupling between the transverse oscillating electrons and the quasistatic ions, a mechanism similar to the oscillating two stream instability in the inertial confinement fusion research. The predictions of the mode structure and the growth rates from the theory agree well with the results obtained from the PIC simulations in various regimes, indicating the model contains the essence of the underlying physics of the transverse breakup of the target.

Figure 1

(a) The schematic model of hole boring process by radiation pressure. (b) The physical picture of transverse instability within the high density layer. The $z$ and $y$ axis represent the longitudinal and transverse directions, respectively. The $n_{i1}$ and $E_{y1}$ represent the ion density and the transverse electric field fluctuations, respectively. $f_p$ represents the ponderomotive force.

Figure 2

The relationship between $k$ and $\mathrm{Im}(\omega )$ for the case of ${\gamma }_0=1.5$, ${\omega }_{pe}=6{\omega }_0$, ${\omega }_{pi}=0.13{\omega }_0$.

Figure 3

(a) In the case of $a_0=0.2$, $n_{p0}=10n_c$, the proton density with ripples in the front high density layer and its lineout distribution at $z=10.38c/{\omega }_0$ (the red dotted line). (b) the FFT of the proton density and its lineout distribution at $k_z=0$ (the green dotted line). (c) The relationship between $k_m$ and $a_0$ when $n_{p0}=10n_c$. (d) The relationship between $k_m$ and $n_{p0}$ when $a_0=0.2$. $k_{\text{sim}}$, $k_{\text{est}}$, and $k_{\text{num}}$ are obtained from PIC simulations, from direct numerical solutions of Eq. (3), and from Eq. (6), respectively.

Figure 4

(a) The relationship between ${\gamma }_m$ and $a_0$ at $n_{p0}=10n_c$. (b) The relationship between ${\gamma }_m$ and $n_{p0}$ at $a_0=0.2$. ${\gamma }_{\text{est}}$ and ${\gamma }_{\text{sim}}$ are the estimated and simulation wave numbers of ion density ripples, respectively.

Figure 5

(a)–(b) for $a_0>1$, proton densities of two different scenarios [thick foil case (a) and thin foil case (b)] are presented. (c)–(d) laser pulses with transverse Gaussian profile are used to interact with foils to confirm the usability of the theoretical expressions. $k_{\text{sim}}$, $k_{\text{est}}$, and $k_{\text{num}}$ are obtained from PIC simulations, from direct numerical solutions of Eq. (3), and from Eq. (9), respectively. $d$ represents the thickness of the target.