Acceleration of proton bunches by petawatt chirped radially polarized laser pulses

Results from theoretical investigations are presented which show that protons can be accelerated from rest to a few hundred MeV by a 1-PW chirped radially polarized laser pulse of several hundred femtosecond duration and focused to a waist radius comparable to the radiation wavelength. Single-particle calculations are supported by many-particle and particle-in-cell simulations. Compared with laser acceleration by a similar linearly polarized pulse, the gained energies are less, but have better beam quality. For a suitable initial phase, a particle bunch gets accelerated by the axial component $E_z$ of the laser pulse and, initially focused by the transverse electric field component $E_r$. Beam diffraction finally sets in due to the particle-particle Coulomb repulsion, after interaction with the pulse ceases to exist.

Figure 1

A schematic illustrating the initial conditions of the single-particle interaction with a chirped laser pulse.

Figure 2

Variation of the proton exit kinetic energy with the dimensionless parameter. The laser parameters used are as follows: $P_0=1$ PW, $w_0={\lambda }_0$, $I_0\simeq 1.178\times {10}^{22}$ W/cm${}^2$, $\tau =150$ fs, and ${\lambda }_0=1\mu$m. In the insets we zoom in on parts corresponding to the highest particle kinetic energies achievable for cases of downchirp (left) and upchirp (right).

Figure 3

(a) Single proton exit kinetic energy evolution with space time (through $\eta$) for two values of the dimensionless chirp parameter. (b) The electric field component $E_z$, normalized by $E_0\left(\eta \right)$, sensed in flight by protons whose kinetic energy evolutions are shown in (a). All other parameters are the same as in Fig. 2.

Figure 4

A schematic illustrating the initial conditions for an ensemble of 3000 noninteracting protons prior to interaction with a chirped laser pulse incident upon them from the left.

Figure 5

Three-dimensional (3D) trajectories of 100 protons, chosen at random from the initial ensemble of 3000 distributed uniformly within a disk of radius $0.3{\lambda }_0$ and thickness $0.2{\lambda }_0$ (see Fig. 4) as a result of interaction with a radially polarized laser pulse chirped at $b=-0.00627$. All other parameters are the same as in Fig. 2, and the interaction time corresponds to the interval from $\eta =0$ to $\eta =8\sigma$.

Figure 6

(a) Projections onto the $xz$ plane of four single proton trajectories, all for the case of $b=-0.00627$. (b) A zoom in on the leftmost part of the trajectories shown in (a). The protons were chosen randomly from an ensemble that is described in Sec. 4. All other parameters are the same as in Fig. 2.

Figure 7

Evolution in $\eta$ of an ensemble of 3000 protons, assumed to be noninteracting, initially at rest and randomly distributed within a cylinder of length $L=0.2{\lambda }_0$, radius $R=0.3{\lambda }_0$, centered at the origin of a Cartesian coordinate system and whose axis is oriented along $z$. (a)–(d) Snapshots of the projection of the evolving ensemble onto the $xz$ plane; (e)–(h) snapshots of the projection onto the $xy$ plane. Top to bottom, the pairs of snapshots are for times corresponding to $\eta$ equal to 0, $4.8\sigma$, $5.2\sigma$, and $8\sigma$, respectively. Note that $\eta =0$ and $\eta =8\sigma$ mark the start and end, respectively, of the particle-field interaction. The pulse parameters are the same as is Fig. 2 for $b=-0.00627$.

Figure 8

Same as Fig. 7, albeit for $b=0.00577$.

Figure 9

A schematic illustrating the initial conditions for a 2D underdense plasma prior to interaction with a chirped laser pulse incident upon it from the left.

Figure 10

Density plots of the electron-proton plasma during interaction with a 1-PW, chirped, radially polarized laser pulse of duration $\tau =150$ fs and dimensionless chirp parameter $b=-0.00639$. (a)–(f) are snapshots at instants corresponding to the values of $\eta$ given on them in terms of $\sigma ={\omega }_0\tau /\left(2\sqrt{2\ln 2}\right)$.

Figure 11

Density plots showing (a) the proton distribution, and (b) the electron distribution of Fig. 10b separately. In other words, (a) and (b) here, put together, yield Fig. 10b.

Figure 12

Same as Fig. 10, but for $b=0.00575$.

Figure 13

Same as Figs. 10 and 12, but for $b=0.00925$, and $\tau =100$ fs.

Figure 14

Density plots showing (a) the proton distribution, and (b) the electron distribution of Fig. 13b separately. In other words, (a) and (b) here, put together, yield Fig. 13b.