Plasma solenoid driven by a laser beam carrying an orbital angular momentum

A megagauss quasistatic axial magnetic field can be produced from the interaction of an intense laser beam carrying an orbital angular momentum with an underdense plasma. Three-dimensional ‘particle in cell” simulations and analytical model demonstrate that orbital angular momentum is irreversibly transferred from a tightly focused radially polarized laser beam to electrons without any dissipative effect. A theoretical model describing the individual interaction of electrons with laser shows that particles gain angular momentum during their radial and longitudinal motion in the laser field. The electron rotation and the generated axial magnetic field survive to the end of the laser-plasma interaction and continue over a long time. The agreement between particle in cell simulations and the simplified model identifies routes to increase the intensity of the solenoidal magnetic field by controlling the laser beam characteristics, such as, for example, the orbital angular momentum and/or the pulse duration.

Figure 1

An OAM $l=1$ laser beam helical energy distribution.

Figure 2

(a) Longitudinal, (b) radial, and (c) azimuthal components of the laser electric field computed at the focal point $x_0=46c/{\omega }_0$ in PIC simulations with no plasma.

Figure 3

(a) Longitudinal, (b) radial, and (c) azimuthal components of the laser electric field computed before the focal point at $x=30c/{\omega }_0$ in the PIC simulations with no plasma.

Figure 4

(a) Longitudinal, (b) radial, and (c) azimuthal components of the laser electric field computed after the focal point at $x=63c/{\omega }_0$ in the PIC simulations with no plasma.

Figure 5

Longitudinal orbital angular momentum averaged over all the electron population (black solid curve), over electrons with positive $L_x$ (red solid curve), and negative $L_x$ (green solid curve). Fraction of electron population with positive (red dashed curve) and negative (green dashed curve) $L_x$.

Figure 6

Transversal cut of the electron $L_x$ distribution near $x=30 c/{\omega }_0$ for ${\omega }_{0}t=120$. The dashed black curve displays the field maximum amplitude contour.

Figure 7

Solenoidal magnetic field $B_x$ for ${\omega }_{0}t=120$.

Figure 8

Longitudinal orbital angular momentum ($L_x$) computed at ${\omega }_{0}t=97$ versus the initial electron radial position with (green circle) and without (gray markers) active plasma motion. The red dotted curve and the black circles display the $L_x$ values computed, analytically by using the perturbation theory and numerically, respectively.

Figure 9

Longitudinal orbital angular momentum of electrons versus their initial radial position computed from the numerical integration of motion equations (black circle) and the theoretical prediction according to Eq. (14) (red curve) for $a_0=0.4$ and $\alpha =0.1$. The other laser parameters are identical to the PIC simulations: $w_0=2\mu \mathrm{m}, \tau =6{\tau }_0, l=1$.

Figure 10

$L_x$ versus the electron initial radial position computed with PIC simulations with active plasma (gray dot), with the numerical resolution of motion equations (black circle) and with the perturbative formula given in Eq. (14) (red curve) for $a_0=1$ and $l=-1, \tau =6{\tau }_0, w_0=2\mu \mathrm{m}$.

Figure 11

Longitudinal cut of $B_x$ computed from PIC simulations for (a) $l=-1$ and $\tau =6{\tau }_0$ and (b) $l=1$ and $\tau =12{\tau }_0$ five optical periods after the laser-electron interaction ends. The others laser parameters are kept unchanged.

Figure 12

The electron solenoid with a length $d$, an internal radius $r_0$, and an external radius $r_1$. Electrons are localized in the blue zone.

Figure 13

$L_x$ versus the electron initial radial position computed with the numerical integration of motion equations (black circle) and with the perturbative formula given in Eq. (14) (red curve) for $a_0=0.1$ and $l=1, \tau =6{\tau }_0, w_0=2\mu \mathrm{m}$.

Figure 14

$L_x$ versus the electron initial radial position computed with the numerical integration of motion equations (black circle) and with the perturbative formula given in Eq. (14) (red curve) for $a_0=0.1$ and $l=-1, \tau =6{\tau }_0, w_0=2\mu \mathrm{m}$.

Figure 15

$L_x$ versus the electron initial radial position computed with the numerical integration of motion equations (black circle) and with the perturbative formula given in Eq. (14) (red curve) for $a_0=0.1$ and $l=1, \tau =12{\tau }_0, w_0=2\mu \mathrm{m}$.