# Linear Particle Accelerator

Why not build a small resonance based linear particle accelerator?

### Abstract:

The study of particles, the building blocks of matter, revolves around the ability to study their composition, mainly by accelerating them to high velocities and then colliding them with something. While physicists have had this ability for the better part of a century, constructing this sort of device is normally only in the realm of large institutions with equally large research budgets. However, the concept is simple in principle and an accelerator can thus be designed that can be built without extensive resources.

A linear particle accelerator can be divided into two major subsystems, mechanical and electrical. Mechanically, an accelerator consists of an ion source, a beam line, a target, and a pump system. Two of these components, the beam line and the pump system require special attention. For an accelerator to function properly, a high vacuum must be maintained. The simplest method to achieve such a vacuum is a mechanical pump combined with a cold trap to condense any pump oils or water vapor. At the lower frequencies of a small accelerator, the beam line must be made of a nonconductive material. In order to maintain vacuum, materials that have low out-gassing must be used, leaving only glass. The electrical system consists of a high voltage, high frequency supply and drift tubes. A microcontroller can be used to generate an adjustable waveform, controlling particle acceleration. With proper planning, an accelerator can thus be constructed.

### Discussion:

The earliest particle accelerators were one-stage linear accelerators, driven by a static high voltage source; such an accelerator has its limits, however, as the voltage source will eventually arc over, setting an upper limit its acceleration potential. This obstacle was overcome by Rolf Widerøe with the invention of the resonance accelerator. In such an accelerator, drift tubes are used, alternately connected to ground and a high frequency, high voltage AC power source. With this concept, a particle can be accelerated multiple times, reaching far higher energies than with an electrostatic accelerator. While a particle is within a drift tube, it is electrically shielded and is accelerated in the gaps between tubes. As a particle approaches a drift tube connected to the AC power source, it is accelerated toward the tube; the field then changes polarity while the particle is contained within the tube, and the particle is accelerated away from the tube once it exits. Thus, the particle is accelerated as if the acceleration potential were twice what it actually is.

In order for particles to continue moving once they are accelerated, a vacuum must be maintained within the beam line. In addition, the electric fields of the drift tubes must reach the particles being accelerated; this can be achieved either by using a non-conductive material for the beam line or by placing the drifts tubes within the beam line itself. The simpler method of using a non-conductive material was used, avoiding issues of electrical insulation and vacuum leakage. Plastic, however, cannot be used as it out gasses in a vacuum, eliminating the possibility to use cheap, readily available PVC pipe. Thus, a borosilicate glass pipe, designed for use with steam boilers, was used. This was then connected to a mechanical vacuum pump using copper pipe. A cold trap consisting of a U-shaped pipe and an isopropanol/dry ice solution was placed between the pump and the accelerator to prevent back streaming of pump oil into the beam line.

To power and control the accelerator, electronics were designed and assembled to produce a waveform with a controllable frequency. In order to create both positive and negative voltages, a microcontroller was connected to a RS232 level converter to change TTL voltages to +12V and -12V. These signals were connected to transistors to switch the larger current required by the accelerator. An ignition transformer was then used to convert the low voltage waveform into a 30kV waveform for powering the accelerator. This control board is powered by a standard ATX computer power supply as it provides clean, regulated power at both the 5V required for the majority of the electronic components and the +12V and -12V required by the transformer, all in a cheap, compact package. Ions for the accelerator were created from the atmosphere, mostly nitrogen, through the use of an off-the-shelf 7.5kV DC power source connected to points inserted into the ionization chamber.

As all the particles accelerated are ions, the effectiveness of the accelerator can easily be determined by counting the number of said ions that reach the end of the beam line. In its simplest form, this can be determined with a Faraday Cup. A copper target was placed at the end on the beam line and was connected to ground across a 1MΩ resistor. An analog to digital converter was then used to find the voltage drop across this resistor and thus the current via Ohm’s Law. Measurements were recorded via a microSD card.

### Analysis:

Data collection during the experiment consisted of analog to digital converter measurements in regards to a 1.1V reference potential (x is the analog to digital converter measurement).

$V=x\cdot1.1V$

These measurements were taken across a 1MΩ resistor, allowing one to calculate current by way of Ohm’s Law.

$I=\frac{V}{R}$

By dividing by the charge of an ion, the number of ions accelerated can be calculated.

$n_{ions}=\frac{I}{q_{ion}}$

Combining these points, a formula can be created to convert the sensor readings into the number of ions accelerated.

$n_{ions}=\frac{\frac{1.1V\cdot x}{1\times10^{6}\Omega}}{1.6\times10^{-19}C}$

A review of the data show that the most effective frequency was 125kHz. In addition, this was the frequency at which the data was most consistent, with the least outliers. As frequency decreased, the number of ion hits recorded also decreased. Based on the data collected, 125kHz is the optimal frequency for operating the accelerator with ions generated from the air, mostly nitrogen. The data collected is incomplete, however, as optimal frequency was found to be at the edge of the data set. A frequency generator capable of creating higher frequency waveforms could be used to verify the data collected by expanding the upper limit of the data set, allowing a peak to be determined.