Čerenkov Radiation Application

Last week I gave a quick run-down of the justification of Cherenkov radiation from classical electrodynamics.  In practice, this effect is the centerpiece of many experiments, and I'll run through how and what we need to know in this post.

We recall the velocity of the charge particle must exceed the phase velocity of the E&M field to emit Cherenkov radiation, or with index of refraction n:



Cherenkov radiation comes in the form of an electromagnetic shock wave, a conical wavefront formed following the particle, emitted at angle:



Since we'd like to pick up this radiation in photomultiplier tubes to observe the effect and therewith the incident charge particle, it's good to know how many photons to expect.  Following the math of the last post on Cherenkov radiation (or just following along in Jackson), we take the energy differential over frequency and divide by de Broglie's h bar omega and then by L we get the number of photons per unit length:



Cherenkov radiation contributes to the mechanism of several types of particle detectors, including electromagnetic calorimeters and non-scintillating hodoscopes; there are two types of detectors specifically designed to directly take advantage of the Cherenkov radition emitted by high energy charge particles: threshold Cherenkov detectors and differential Cherenkov detectors.

In the threshold Cherenkov detector, the medium in the tank is chosen carefully for a refractive index that indicates the passage of charge particles that exceed a given velocity threshold.  Usually this is done with a gas such as hydrogen, nitrogen or carbon dioxide, and further control of the refractive index comes through the pressure of the gas in the tank.

The differential Cherenkov detector allows the measurement of a particle's velocity while rejecting particles outside a given mass range.  This is accomplished by accepting a small annulus around the track of incident particles at some angle theta.  This corresponds, at a given refractive index, to a velocity resolution:



The minimum velocity resolution is often constrained by the minimum angular resolution, which tends to be limited by dispersion in the slit.

Sources:  Leo's Techniques and Fernow's Intro to Experimental Particle Physics