Laser accelerated protons captured and transported by a pulse power solenoid

Using a pulse power solenoid, we demonstrate efficient capture of laser accelerated proton beams and the ability to control their large divergence angles and broad energy range. Simulations using measured data for the input parameters give inference into the phase-space and transport efficiencies of the captured proton beams. We conclude with results from a feasibility study of a pulse power compact achromatic gantry concept. Using a scaled target normal sheath acceleration spectrum, we present simulation results of the available spectrum after transport through the gantry.

Figure 1

Dosimetric film stack illustrating the recording of laser accelerated protons and the decrease in divergence angles $\Theta$ for more energetic protons.

Figure 2

Direct measurement of laser accelerated protons from a single PHELIX laser pulse. The low energy protons deposit a larger dose and have a larger beam profile than the higher energy protons.

Figure 3

Top: Processed results of the data presented in Fig. 2 (black solid curve, top and right axes, includes 5% radiochromic film imaging spectroscopy error bars and 50% shot-to-shot error bars) along with a scaled (predicted) TNSA spectrum with maximum energy of 250 MeV (red dashed curve, bottom and left axes). Bottom: Maximum beam divergence as a function of proton energy.

Figure 4

Experimental setup: The windings of the solenoid begin 95 mm from the target. Laser-target alignment optics and dosimetric film are positioned under vacuum using motor stages.

Figure 5

Plot of measured current through the solenoid as a function of time. The solenoid is pulsed at time $t=2.85\mathrm{ms}$, and the laser is pulsed at $t=3.20\mathrm{ms}$. The current at the time of the laser pulse is 9.85 kA as indicated by the green dashed line and can be considered static since the acceleration time is on the ps time scale and propagation time through the magnetic field is on the ns time scale.

Figure 6

Radiochromic film images: The films record the transverse position of the protons after they have been transported through a 7.2 T (top) and 8.5 T (bottom) solenoidal field. Proton energies corresponding to Bragg peak dose depositions are shown at the bottom of each film, and arrows point to areas of limb brightening.

Figure 7

Illustration of the generation of film response to protons from simulated data. (A) Proton density in a simulated layer of film. (B) Dose deposited from the protons in the left image. (C) Final result after weighting the deposited dose with the optical density response of the film.

Figure 8

Simulated film response from proton transport through fields of (A) 7.2 T and (B) 8.5 T for the first three films in each stack.

Figure 9

(A) Phase-space plot for all protons at or above 6.7 MeV for 8.5 T (i.e. protons incident on film layer #2 in Fig. 8). The green points highlight the 6.7 MeV protons. (B) A projection of the phase-space plot onto the $x$ axis illustrates the proton density across the focal spot.

Figure 10

A phase-space plot for all laser accelerated protons passing through the 8.5 T field. The green points (enlarged in lower image) highlight the $13.75\pm 0.1\mathrm{MeV}$ protons. The chromatic aberration results in divergent beams (yellow points), collimated beams (green points), focused beams (light-purple points), and beams that diverge after a focus (dark-purple points) at the film detector.

Figure 11

Simulation of particle densities within dosimetric film layers illustrating the effect of higher order aberrations in the magnetic field.

Figure 12

Divergence angles ${\Theta }_x$ of protons after passing through the 8.5 T field of the solenoid. The color density indicates the transport efficiency $d\eta /(d{\Theta }_{x}dE)$ for a single energy and single angle while the top is a projection showing the total transport efficiency $d\eta /dE$ for a single energy across all angles. As governed by the 8.5 T field, 13.75 MeV protons are collimated with near collimation of the $13.75\pm 1.25\mathrm{MeV}$ protons.

Figure 13

Proton spectra within various angular envelopes after the 8.5 T solenoid field. The $1\sigma$ and $2\sigma$ confidence band normalized emittances for the protons within 1 mrad are 2.5 and $10.2\pi \mathrm{mm}\mathrm{mrad}$.

Figure 14

Simulation results from feasibility study: Proton tracking of the scaled TNSA spectrum of Fig. 3 through a pulse power solenoid coupled to a theoretical achromatic pulse power gantry. The large image shows the $\mathbf{z}[\mathrm{m}]$, $\mathbf{y}[\mathrm{m}]$ profile while the inset in the top left shows the $\mathbf{x}[\mathrm{m}]$, $\mathbf{y}[\mathrm{m}]$ profile. The quadrupole gradients are up to $400\mathrm{T}/\mathrm{m}$ over 5 cm or less, and the dipole fields are 8.6 T.

Figure 15

Simulation of the proton spectrum after capture and collimation with a 32 T solenoidal field (blue, dotted curve) and transport through the simulated gantry presented in Fig. 14 (green, solid curve). When the solenoid field is set to zero, the spectrum emerging through the gantry is below ${10}^4$ protons per MeV.