# Building a simple improvised electron gun from common of the shelf components

28 Apr 2021 - tsp
Last update 07 Jul 2021

## Introduction

So everyone knows these days where you just need a improvised (telefocus) electron gun that can provide a reasonable amount of current - in case of the one described in this blog post up to 2 mA since that was the limit of the available FUG HCP 14-6500 power supplies - for some physics experiment or an improvised electron microscope. This idea emerged since I played around with a variety of electron sources for some quantum physics experiment - and since it sounded too simple there was no reason to not try it out.

Since I worked with some sophisticated optics and special tungsten cathodes designed to be used in scanning electron microscopes which didn’t produce really high currents the idea was simple - use a hot cathode in a triode assembly and try to source as much current as possible. For a first estimation a metalized phosphor screen was used as target - this phosphor screen had been salvaged from an old damaged oscilloscope tube already for another project.

## Setup

The voltages for the triode had been chosen to be larger (more negative) than $-2 kV$ at the cathode as well as the Wehnelt assembly. The Wehnelt was kept a few Volts more negative as the cathode. The target had the same potential as the vacuum chamber that the assembly had been put into - that has been chosen (or was already fixed) at ground potential. This made design much more easy - and is also the same setup used for another more sophisticated project. Since I’m using a directly heated filament I had to heat it using direct current instead of alternating current. The heating voltage has been sourced from an insulation transformer with primary side voltage regulation, has been rectified and smoothed using a $40 mF$ capacitor bank (note that this bank has been biased to more than $2 kV$ too - and don’t forget that’s enough capacity to be lethal when touched, don’t forget bleeder resistors across the terminals and calculate the time required to discharge to safe levels) and then supplied directly to the cathode. Note that the wires should have a larger diameter since they also contribute to the total resistance of the system.

The cathode material itself is a tungsten wire doped with Rhenium - thus a work function around $4.5 eV$ and a Richardson constant around $60$ to $100$ with an upper working temperature up to around $3200 K$ (more theory is available in another blog post). This cathode has been simply salvaged from a 12V halogen lamp because these are using filaments that are wound to form a large surface area - and they are available at every street corner.

To extract the cathode from the lamp I tried to use the procedure described in a forensics paper but as it turned out it was more simple to put the lamp inside a plastic bag (to catch any quartz glass shrapnel - be careful and don’t hurt yourself, the lamps basically explode and one does not see quartz glass on x-ray images in the hospital) and crush the lamps slowly using a machine vice. One then only has to be careful when unpacking the remains of the lamp and then remove the remaining glass except for the post using a file.

To mount the cathode - and also as a Wehnelt cylinder - a standard copper tube commonly used in heating infrastructure has been used and clamped into an aluminum block. The hole at the lower end as well as the taper has been formed by the shape of the used $12mm$ drill. The hole at the front has been deburred using a file though since sharp edges are usually a source of corona discharge due to high electric fields. Two mounting screws are used to clamp the remains of the capped halogen lamp inside the copper tube using two M4 steel (A4) screws.

The whole assembly is mounted on two M6 screws - the heads are pushed into a PLA plastic stand that will also be used during testing to insulate the feet since they’re kept at the same potential as the Wehnelt assembly. The extraction electrode is realized using a 4 mm thick washer for M8 screws that has been mounted with a PLA holder directly below the Wehnelt assembly.

The wiring has been done using standard copper wire - the Washer has been attached simply by twisting the wire around the washer, the Wehnelt assembly is using a screw (and after the photos have been made a crimp connector for a screw terminal). The connections between the halogen lamp post and the wires have also been made using plugs formed out of simple not fully crimped butt connectors - that have been additionally insulated using Kapton tape.

At the end the whole assembly has been placed into a small testing vacuum chamber and pumped down to around $10^{-4} mbar$ till cathode conditioning started. Conditioning has been done as usual - simply ramping up current slowly over about 20 minutes. This should remove any adsorbed water vapor from the surface of the tungsten cathode. Just keeping an eye on the pressure is a good idea. In addition high voltage has been ramped up in parallel as an insulation test with a set current limit around $0.1 \mu A$.

After reaching a pressure of around $10^{-6} mbar$ the cathode has been heated using around $1.5A$ to $2 A$, the exact current depends on the used lamp type. As long as one operates in thermally limited mode one will see a radical increase in emission current as long as one increases the heating current. As soon as one enters space charge limited mode the emission current does not increase any more when one increases the filament temperature. In this case one might want to increase acceleration voltage - just keep in mind the insulation ratings of your cables as well as the insulation ratings of your vacuum pass-throughs. Also keep an eye on the pressure of the chamber - if PLA reaches temperatures above around 70 degrees it will evaporate - you really don’t want to have residue of plastic inside your turbo- or membrane pumps, you’d smell this many weeks long and if you’re doing any precision measurement you’ll have to clean the chamber again. Since the cathode itself operates up to 3000K one should really be careful with operation duration as well as thermal stability of the PLA parts.

Also don’t forget that higher acceleration potentials (starting around $10 kV$) are also producing x-rays. Be sure to know what you’re doing when it comes to ionizing radiation.

The final beam current achieved with this rough hacked setup has been around $2 mA$ due to limited power supplies. Usually this type of cathodes should be able to supply an substantial amount of power.

# Speed of emitted electrons

As a first approximation one can assume that electrons are accelerated from zero velocity - this is of course not totally true since the velocities of electrons emitted from a thermal cathode surface are distributed according to the Maxwell-Boltzmann distribution.

## Approximating speed of electrons for lower acceleration voltages

In the non relativistic case one assume that the potential energy of the electric field $E_{el} = q * U$ is directly transformed into kinetic energy $E_{kin} = m v^2$ of the particle:

[ E_{el} = E_{kin} \\ q * U_a = m * v^2 \\ v = \sqrt{\frac{q U_a}{m}} ]

Thie description holds for acceleration voltages up to around $2 kV$. For higher voltages - or periodic acceleration structures like linear accelerators or acceleration cavities - one should use a relativistic description.

## Approximating speed of electrons for acceleration voltages larger than 2 kV

For acceleration voltages above $2 kV$ it’s advisable to use a relativistic expression As is already known the total kinetic energy of an electron is determined by the difference of it’s relativistic mass and it’s rest mass:

[ E_{kin} = m_{rel} * c^2 - m_e * c^2 ]

The relativistic mass is known to be

[ m_{rel} = \gamma * m_e \\ \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} ]

Whenever a charge (for an electron $q = e$) passes through an electric potential $U_a$ the potential energy is transformed into kinetic energy

[ U_a * e = E_{kin} ]

Inserting the relativistic kinetic energy one simply obtains

[ \to U_a * e = m_{rel} * c^2 - m_e * c^2 \\ \to U_a * e = m_e * c^2 * \left(\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} - 1\right) \\ \to \frac{U_a * e}{m_e * c^2} + 1 = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} \\ \to v = c * \sqrt{1 - \left(\frac{m_e * c^2}{U_a e + m_e c^2}\right)} \\ \to v = c * \sqrt{1 - \frac{1}{\left(1 + \frac{U_a e}{m_e c^2}\right)^2}} ]