Gas-Stopping Cyclotron

Problem Description

Gas-stopping cyclotrons have been used to decelerate high- or medium-energy particles to low energy for use in low-energy experiments such as those used to study material surface properties. These devices have been used to decelerate muons, pions, and antiprotons. A new device is being designed for ions.

Typical stopping devices (or stoppers) are linear blocks of material, such as a gas chamber, which work well for lower-energy and higher-mass particles. However, for higher-energy and lower-mass particles, linear stoppers exhibit large stopping ranges in the material, which result in a very long stopped-particle distribution and subsequently long extraction times from the gas.

To reduce the physical size of the beam when it has stopped, the gas-stopping cyclotron was proposed. In principle, the particles spiral into the center of a cyclotron-like field, losing energy in a moderating material, such as helium or hydrogen gas. Regardless of the stopping range of the particles in the gas, the gas stopping cyclotron stops the particles in a much smaller distribution near the core of the cyclotron field. The resulting distribution can then be extracted out of the cyclotron in the direction normal to the cyclotron plane.

The energy loss mechanism is primarily ionization of the moderating gas. The ionized plasma that is produced can then interfere with extraction fields needed to pull the stopped particles out of the gas.

Input File Features

In a real gas-stopping cyclotron, the fields must be defined in 3D and must provide focusing into the mid-plane of the cyclotron for the particles as they spiral into the center. Without focusing into the mid-plane, particles will scatter in the moderating gas and eventually scatter out of the cyclotron itself. This example shows a 2D approximation to the gas-stopping cyclotron, using only a uniform magnetic field in the z-direction while the beam particles are defined only in the mid-plane.

We define Species to represent the beam particles (\(\mu\) ⁺, in this case) and the ionized gas particles. We assume the neutral gas is atomic hydrogen (for simplicity), which we represent by a Fluid. The ionized gas is represented by an electron Species and an H⁺¹ hydrogen-ion Species.

The energy loss, multiple scattering, and energy straggling in the hydrogen gas is handled by the nullBgAbsorber NullInteraction in the MonteCarloInteractions block. Radioactive decay of the muons into electrons (the neutrinos not being kinetically modeled) is handled by the oneBodyVADecay Interaction. Impact ionization of the hydrogen gas by the beam and decay electrons is handled by the impactIonization Interaction, and to deal with the massively large numbers of particles produced by the ionization processes, we use the selfCombination Interaction to combine like-species particles together when more large numbers of particles start to accumulate in a single cell.

Lastly, we use the speciesNumberOf and speciesEnergy History blocks to monitor the evolution of the beam and the ionization-produced macroparticles.

Running the Simulation

Start VorpalComposer and select File -> Clone Example. Highlight Solving Classical Physics Problems and then select Next. Highlight Gas-Stopping Cyclotron and then select Choose. Create a new folder and then select Choose.

Alternatively, save the VORPAL input file, gasStoppingCyc.pre, and open in VorpalComposer.

The file should be displayed in the right pane of the Setup window. Click on the Save and Process Setup button in the lower right corner. Proceed to the run window as instructed. To run the file, click on the Run button in the lower left corner of the window. You can see the real time output of the run in the right pane.

Viewing the Output

After the run has completed, view the data written by VORPAL to HDF5 files by clicking on the Visualize tab on the left.

To view the muon beam as it spirals into the cyclotron core, select the ‘muons’ from the Particle Data variable window. Then, click on the Dump selector arrow at the bottom right and use the right and left arrow keys to move to the next dump and see how the beam changes over time. To view the ions and electrons in the simulation, select the ‘H1’ and ‘electrons’ variables as well.

To view the history data, click the History tab on the left half of the viewer window (below the Fields tab). View three histories simultaneously by selecting ‘muonEnery’, ‘muonNumber’, and ‘protonNumber’ from the three drop-down menus. The ‘muonEnergy’ plot shows the total energy of the muon beam, which grows as muons are added to the simulation and then decreases as they lose energy in the hydrogen gas. The ‘muonNumber’ plot shows the number of macroparticles in the muon beam, which grows as muons are added to the simulation and then slowly decreases as muon decay. The ‘protonNumber’ (which looks identical to the ‘electronNumber’) plot shows the number of proton macroparticles growing due to ionization events and then leveling off as the self-combination interactions keep the total numbers low to prevent the simulation from getting bogged down.

Results

The figure shows the distribution of the muon beam at the end of the VORPAL simulation. This does not run the beam long enough to get into the core of the cyclotron.

VorpalComposer view of the muon beam at the end of the simulation

The figure shows the plots of the muon number, muon energy, and proton number throughout the simulation.

VorpalComposer view of the history data