Measuring Electron Beam Currents

Question

When it comes to measuring electron beam currents with a Faraday Cup (or any that will pick up electrons and act as an anode), primarily AC and transient signals, my understanding is that one can:

(1) add an ammeter in series

(2) add a resistor (or capacitor) in series and measure the voltage across that resistor

(3) use a current loop and measure via induction.

It seems like there are pro's and con's to all of these, but I'm wondering, when trying to measure the current in an electron beam in a vacuum, which of the three above methods (if any) is the proper or ideal way to do this? Where does the impedance of the circuit come into this? If I want to use an oscilloscope to get time-resolved measurements, how does this come into play? If the anode/Faraday Cup is biased to prevent secondary electrons, how does this affect things?

Answer 1

I was involved (in the 1990s) in designing Gas mass spectrometers and the preferred method for dealing with the curved ionic "beam" (due to gas atomic/molecular mass and the applied magnetic flux density) was an earthed plate with a slot in it - the curved beam (when at the correct radius due to the precise mass) went thru the slot and hit an electrode which directly fed a transimpedance amplifier.

Some amount of series resistance was tried (mainly because it was felt the transimedance amplifer might be protected by it) but it neither made it more reliable (it was fairly reliable anyway) nor seemed to reduce the effectiveness of the amplifier.

So, the two methods that appeared to work equally good are transimpedance amplifiers and a regular inverting amplifier using op-amps. I can't say if other methods work based on my direct experiences.

Answer 2

This depends a lot on the structure of your beam.

(1) add an ammeter in series

This may work if the current is high enough to be measured and if the current is quite constant over time to overcome the inertance of the amp-meter. Note that if you open the circuit to add/remove the amp-meter, the anode charges up.

However, currents of a few nA can be measured with good equipment, so this is a method e.g. for the Franck-Hertz experiment where the kinetic energy of the electrons is in the range of 5eV.

(2) add a resistor in series and measure the voltage across that resistor

This is similar to (1), but you do not open the circuit to measure. Since you can not measure voltages of some nV, but of some µV, you need some resistance. So, the anode may charge up and you start to deflect the electrons. But if the beam energy is high enough, that does not matter

(3) use a current loop and measure via induction

This again may cause a voltage on the anode and only works for non-constant beam structures.

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What is often used in a photomultiplier tube is this:

^{simulate this circuit – Schematic created using CircuitLab}

Here, the anode is connected to GND via a large 10-100kOhm resistor to prevent charging if nothing is connected. The internal 50Ohm of the oscilloscope is used for measurement, the additional 50 Ohm at the output of the PMT is to match the impedance of the coax cable.

I used this to measure pulses of ~2ns length and ~5V amplitude in the scope. As the accelerating voltage is some hundred volts, this does not matter.