Performance of solenoids versus quadrupoles in focusing and energy selection of laser accelerated protons

Using laser accelerated protons or ions for various applications—for example in particle therapy or short-pulse radiographic diagnostics—requires an effective method of focusing and energy selection. We derive an analytical scaling for the performance of a solenoid compared with a doublet/triplet as function of the energy, which is confirmed by TRACEWIN simulations. Generally speaking, the two approaches are equivalent in focusing capability, if parameters are such that the solenoid length approximately equals its diameter. The scaling also shows that this is usually not the case above a few MeV; consequently, a solenoid needs to be pulsed or superconducting, whereas the quadrupoles can remain conventional. It is also important that the transmission of the triplet is found only 25% lower than that of the equivalent solenoid. Both systems are equally suitable for energy selection based on their chromatic effect as is shown using an initial distribution following the RPA simulation model by Yan et al. [Phys. Rev. Lett. 103, 135001 (2009].

Figure 1

TRACEWIN envelopes for equivalent solenoid (top) and triplet (center and bottom) solutions at 2 MeV.

Figure 2

Comparison of triplet and solenoid systems as a function of energy, where theory focal lengths have been made equal by adjusting the solenoid B field; ${\mathrm{B}}_s^{*}$ (dashed) from theory and ${\mathrm{B}}_s^{\mathrm{TW}}$ (continuous) from TRACEWIN.

Figure 3

Density plots for TRACEWIN obtained reference cases for equivalent solenoid (top) and triplet (center: $x$; bottom: $y$) focusing.

Figure 4

Simulated spectral yield of protons as a function of energy and for different capture cone angles $\Omega$, with bi-Gaussian fit (continuous line).

Figure 5

Density plots for RPA distribution in equivalent solenoid (top) and triplet (center: $x$; bottom: $y$) systems adjusted to 220 MeV.

Figure 6

Transverse (normalized and bunch averaged) rms emittances for triplet case.

Figure 7

Loss profiles for RPA distributions in the equivalent solenoid (top) and triplet (bottom).

Figure 8

Transmission of solenoid and triplet as function of an upper cutoff (divergence limit) of the injected particles. The transmission is in % of the particles in the original untruncated distribution.

Figure 9

Selected energy profiles (normalized to unity) for equivalent solenoid ($R_A=3\mathrm{mm}$) and triplet systems ($R_A=2.7\mathrm{mm}$). Top: initial; center: solenoid; bottom: triplet.