Electromagnetic Simulations of Linear Proton Accelerator Structures Using Dielectric Wall Accelerators

Proton accelerator structures for medical applications using Dielectric Wall Accelerator (DWA) technology allow for the utilization of high electric field gradients on the order of 100 MV/m to accelerate the proton bunch. Medical applications involving cancer therapy treatment usually desire short bunch lengths on the order of hundreds of picoseconds in order to limit the extent of the energy deposited in the tumor site (in 3D space, time, and deposited proton charge). Electromagnetic simulations of the DWA structure, in combination with injections of proton bunches have been performed using 3D finite difference codes in combination with particle pushing codes. Electromagnetic simulations of DWA structures includes these effects and also include the details of the switch configuration and how that switch time affects the electric field pulse which accelerates the particle beam. INTRODUCTION DWA-based structures have the advantage over conventional linear accelerator structures of having a high gradient present at the accelerator’s beampipe wall since the geometry of the DWA reduces the spatial overhead. This allows the wall electric field to be the predominant factor in determining the on-axis accelerating field. However, such designs have typically experienced a parasitic effect [1] which reduced the acceleration field due to the closure of the magnetic field lines in undesirable planes. The profiled dielectric radial transmission line based Blumlein structure presented here exhibits a constant impedance and magnetic field lines that close in the plane thus preventing the parasitic effect and allowing for a square-wave operation consistent with standard transmission line theory. PROFILED DIELECTRIC GEOMETRY Consider a profiled radial line with a dielectric permittivity profile [2], εr(r), which obeys: r r max r 2 Then applying this to the standard radial transmission line equation [3] yields an impedance, Z(r), which is: Z(r) 0 r 0 r r d 2 r ≈ 60 r d r 60 max d a and is constant with respect to radius. Note that εmax limits the maximum dielectric permittivity in the configuration, a is the inner radius of the configuration, d is the transmission line thickness, c is the speed of light in vacuum, and r is the radial coordinate. Since the direction of propagation is radial, and the electric field points from the lower transmission line plate to the upper transmission line plate, then the magnetic field is azimuthal. Setting nominal values for the above parameters yields Figure 1. 0.04 0.06 0.08 0.1 0.12 0.14 10 20 30 40 50 0 0.025 Figure 1: Using nominal values for the permittivity in the profiled radial line versus radius (in meters) given εmax = 47.6, a = 25mm, and d = 1mm, yields Z(r)=0.347Ω. From this dielectric constant, the radial velocity and position at time t follows from: v(r) c r c max r a dr dt r(t) aect/a max then inverting, yields: t(r) a max c ln r a However, for conventional fabrication techniques it is envisioned that a discrete graded dielectric profile would be used to construct the profiled dielectric utilized in the radial line as shown in Figure 2. Figure 2: Typical radial grading process for discrete dielectric layers as used in the profiled radial line. As a result of the grading process, the extents of the permittivity profile have to be adjusted such that the TUPAS058 Proceedings of PAC07, Albuquerque, New Mexico, USA 04 Hadron Accelerators 1784 A14 Advanced Concepts 1-4244-0917-9/07/$25.00 c ©2007 IEEE extents across the material allow for the same propagation times. By adjusting the dielectric constants such that the integral over the span of each dielectric subsection is equalized, the resulting permittivity profile is obtained and is shown in Figure 3. 0. 03 0 0. 03 7 0. 04 4 0. 05 4 0. 06 5 0. 07 9 0. 09 5 0. 11 6 0. 14 0 40.0