Calculate Drift Tube Length & Size for Accelerators

[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.

 

[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:

http://www.accsys.com/about/history.html

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;

http://www.cockcroft.ac.uk/education/academic0607.html

.

 

[AllHailOdin]

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:

http://www.accsys.com/about/history.html

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;

http://www.cockcroft.ac.uk/education/academic0607.html

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).

 

[Bob S]

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).

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 L_n = β_nλ. Here, the velocity of the particle at the nth drift tube is v = β_nc, 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

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

 

[pmacias]

I can provide you with the information you need to calculate the drift tube length and size for accelerators. The length and size of drift tubes in accelerators are determined by several factors, including the desired energy of the particles being accelerated, the strength of the magnetic field, and the desired frequency of the particles' oscillations.

To calculate the length of the drift tube, you can use the following formula:

L = (mv^2)/(qB^2)

Where L is the length of the drift tube, m is the mass of the particles being accelerated, v is the velocity of the particles, q is the charge of the particles, and B is the strength of the magnetic field.

To calculate the size and spacing of the drift tubes, you will need to consider the frequency at which the particles are driven. The formula for the frequency of a drift tube is:

f = (1/2π)(qB/m)

Where f is the frequency, q is the charge of the particles, B is the strength of the magnetic field, and m is the mass of the particles.

Based on the desired frequency, you can then determine the size and spacing of the drift tubes to ensure that the particles are properly accelerated and guided through the accelerator.

I hope this information is helpful to you in your calculations. If you need further assistance, please do not hesitate to ask.