# Formula for Drift Tube

1. Jun 22, 2010

### AllHailOdin

I was wondering if anyone knew the formulas uses to calculate the length and size and spacings of the drift tubes used in accelerators, and the formula used to calculate the frequency the tube is driven at.

Edit, looks like I put this in the wrong section, hopefully someone can move it.

Last edited: Jun 22, 2010
2. Jun 22, 2010

### tyroman

Hi AllHailOdin! Welcome to PF!

The lengths of the drift tubes in a LINAC are a function of the RF frequency being used to accelerate the ions. They (the tubes) shield the ions inside for one-half of each cycle of the field and must therefore be made progressively longer as the plasma stream is accelerated.

The ion stream is accelerated in the gaps between drift tubes and the distance from the midpoint of one gap to the midpoint of the next gap is given by;

½ ν /c · c/f ≡ ½ β λ

A good general history of linacs is here:

A more mathematical treatment of linac design is contained in lecture notes (.pdf's) from "Linear Accelerators: Theory and Practical Applications R.Jones" on this page;

.

Last edited by a moderator: May 4, 2017
3. Jun 22, 2010

### AllHailOdin

So if the tubes act as a faraday cage for 1/2 the frequency cycle, then that would mean the higher the frequency the shorter you can make the tubes ? But as the ion accelerates faster the tubes have to get progressively longer. So the diameter of the tubes don't matter much ?

so

½ ν /c · c/f ≡ ½ β λ

v = Voltage in Volts ?
c = ? Current in Amps maybe ?
f = Frequency in Hertz ?

and I don't recognize the symbols of the second half (≡ ½ β λ).

Last edited by a moderator: May 4, 2017
4. Jun 23, 2010

### Bob S

The above formula is correct for the "electrostatic" Wideroe linear accelerator, where the rf voltage is applied directly to alternate drift tubes. Modern (Alvarez) drift tube linacs (DTLs) are standing wave linacs with grounded drift tubes in a large tank with a resonant longitudinal RF field. In this case the spacing between gaps is Ln = βnλ. Here, the velocity of the particle at the nth drift tube is v = βnc, and the rf frequency is f = c/λ. See page 22 of

http://www.cockcroft.ac.uk/education/PG_courses_2006-7/RJ_linacs_2007/Linacs_Week_1-Vers2.1.pdf [Broken]

The Alvarez DTLs often have 50 or more drift tubes in a single tank. Each grounded drift tube has a focusing or defocusing magnetic quadrupole inside.

Bob S

Last edited by a moderator: May 4, 2017