Focusing of Relativistic Electrons in Dense Plasma Using a Resistivity-Gradient-Generated Magnetic Switchyard

A method for producing a self-generated magnetic focussing structure for a beam of laser-generated relativistic electrons using a complex array of resistivity gradients is proposed and demonstrated using numerical simulations. The array of resistivity gradients is created by using a target consisting of alternating layers of different $Z$ material. This new scheme is capable of effectively focussing the fast electrons even when the source is highly divergent. The application of this technique to cone-guided fast ignition inertial confinement fusion is considered, and it is shown that it may be possible to deposit over 25% of the fast electron energy into a hot spot even when the fast electron divergence angle is very large (e.g., 70° half-angle).

Figure 1

Sketch of the material structuring employed in the resistivity-gradient-generated magnetic switchyard concept. Red regions are of higher resistivity (i.e., higher $Z$ in high temperature regime) than the blue regions. The structure is axisymmetric about the $x$ axis.

Figure 2

(a) Plot of atomic $Z$ used in simulation, (b) plot ${log}_{10}(\rho )$ used in simulation with $\rho$ in units of $\mathrm{g}{\mathrm{cm}}^{-3}$. Both plots are slices through the $x\mathrm{\text{−}}y$ midplane of the domain, with the system being axisymmetric about the $y=z=100\mu \mathrm{m}$ line.

Figure 3

Results from 3D hybrid simulation. All plots are in $x\mathrm{\text{−}}y$ midplane: (a) Plot of ${log}_{10}$ fast electron density (${\mathrm{m}}^{-3}$) at 6 ps; (b) plot of $B_z$ component of magnetic flux density (T) at 6 ps.

Figure 4

Results from 3D hybrid simulation. Plots of fast electron angular distribution, $dN/d\Omega$, in three different radial ranges (as indicated) for $97<x<100\mu \mathrm{m}$. Note that $\theta$ is the angle with respect to the $x$ axis. The source function is a constant up to 70°.

Figure 5

Results from 3D hybrid simulation. All plots are in $x\mathrm{\text{−}}y$ midplane in DT fuel region ($x>110\mu \mathrm{m}$): (a) Plot of ion temperature (eV) in DT fuel region at 20 ps; (b) plot of ion internal energy density ($\mathrm{J}{\mathrm{m}}^{-3}$) in DT fuel region at 20 ps.