Higher order mode beams mitigate halos in high intensity proton linacs

High intensity proton linacs (HIPLs) for applications such as Accelerator Driven Reactor Systems (ADRS) have serious beam dynamics issues related to beam halo formation. This can lead to particle loss and radioactivation of the surroundings which consequently limit the beam current. Beam halos are largely driven by the nonlinear space-charge force of the beam, which depends strongly on the beam distribution and also on the initial beam mismatch. We propose here the use of a higher order mode beam (HOMB), that has a weaker nonlinear force, to mitigate beam halos. We first show how the nonlinear space-charge force can itself be exploited in the presence of nonlinear solenoid fields, to produce a HOMB in the low energy beam transport (LEBT) line. We then study the transport of such a beam through a radio frequency quadrupole (RFQ), and show that the HOMB has a significant advantage in terms of emittance blow-up, halo formation and beam loss, over a Gaussian beam, even with a finite initial mismatch. For example, for the transport of a 30 mA beam through the RFQ, with an initial beam mismatch of 45%, the Gaussian beam sees an emittance blow-up of 125%, while the HOMB sees a blow-up of only 35% (relative to the initial emittance of $0.2\pi \mathrm{mm}\text{−}\mathrm{mrad}$). Similarly, the beam halo parameter and beam loss are 0.95 and 25% respectively for a Gaussian beam, but only 0.35 and 15% for a HOMB. The beam dynamics of the HOMB agrees quite well with the particle-core model, because of the more linear space-charge force, while for the Gaussian beam there are additional particle loss mechanisms arising from nonlinear resonances. Therefore, the HOMB suppresses emittance blow-up and halo formation, and can make high current ADRS systems more viable.

Figure 1

Schematic of the beamline transporting a 50 keV, 30 mA proton beam from the ion source to the 3 MeV RFQ.

Figure 2

(a) Transverse particle density distribution of the proton beam at the exit of the LEBT, (b) $r$-$z$ particle density plot in the LEBT, showing the formation of the hollow beam in the nonlinear solenoid field.

Figure 3

Line-out of the horizontal density distribution of the HOMB, along with fits to various higher-order Laguarre-Gauss modes.

Figure 4

(a) Normalized emittance (RMS) at the LEBT output as a function of the (compensated) beam current, for four different beam distributions, (b) phase space (left) and coordinate space (right) distributions at the LEBT exit for an initial Gaussian beam of current $500\mu \mathrm{A}$ (below threshold) and (c) phase space (left) and coordinate space (right) distributions at the LEBT exit for an initial Gaussian beam of current $800\mu \mathrm{A}$ (above threshold).

Figure 5

Variation of the radius of the peak of the density distribution of the HOMB, for Gaussian, parabolic and 4D waterbag and KV initial distributions, as a function of beam current.

Figure 6

Variation of the space-charge force along the radial direction for a Gaussian beam for different beam current superposed with the solenoid force along the radial direction, at the point of formation of the HOMB.

Figure 7

For the Gaussian and HOMB distributions, variation as a function of initial beam mismatch of, (a) transverse emittance, (b) transverse halo parameter, (c) longitudinal emittance, and (d) longitudinal halo parameter, all calculated at the exit of the RFQ.

Figure 8

Tune depression for the Gaussian and HOMB along the RFQ.

Figure 9

(a) Damping of the envelope oscillations, and (b) growth of the transverse rms normalized emittance, along the RFQ, for an initial mismatch of 30% and (c) growth of rms longitudinal emittance along RFQ for the mismatch of 30%.

Figure 10

Initial distribution of the lost particles for the (a) Gaussian, and (b) HOMB, with zero initial mismatch, and for the (c) Gaussian and (d) HOMB, with 30% mismatch.

Figure 11

Plots of the $x$-$y$ tunes of lost particles, (a) Gaussian beam, no mismatch, (b) HOMB, no mismatch, (c) Gaussian beam, 30% initial mismatch, (d) HOMB, 30% initial mismatch.

Figure 12

Histogram of particle loss as a function of distance down the RFQ, for the Gaussian and HOMB, for a mismatch of 30%.

Figure 13

Phase space trajectory of a lost particle along propagation direction in: (a) $x$$x\prime$ and (b) $y$$y\prime$. It can be seen that the particle remains confined in $x$ but is lost in $y$.

Figure 14

RFQ potential at a given longitudinal position and at a given time. The potential is saddle-shaped, explaining the behavior seen in Fig. 13.

Figure 15

x vs energy plot for the (a) transmitted, and (b) lost, particles.

Figure 16

Transverse threshold energy plot as a function of longitudinal position overlapped with particles transverse energy: (a) for the Gaussian beam and (b) for the HOMB.