JUAS 2011

Guided study and tutorial onRF Linear Accelerators

A. Lombardi and JB. Lallement

Transit-time factor

• The energy gain of a particle in a harmonically time-varying field is always less than the energy gain in a constant dc field

• The transit-time factor T is the ratio of the energy gained in the time-varying RF field to that in a dc field

• T is a measure of the reduction in the energy gain caused by the sinusoidal time variation of the field in the gap

2/

2/

2/

2/

),0(

)/2cos(),0(L

L

L

L

dzzE

dzzzET

Pillbox cavityEz

z

TM010 mode in a pillbox cavity Square-wave electric field distribution

Eg

E(z)

-g/2 g/20

For a simple TM010 pillbox cavity of length g with a square profile of the electric field we find E0=Eg if L=g and the transit-time factor becomes

)/(

)/sin(

g

gT

Kilpatrick sparking criterion

What is the maximum surface electric field that we can safely

achieve in linac cavities? We can go up to the electric

breakdown limit usually expressed in terms of Kilpatrick sparking

criterion.

• Electric field applied to a metal surface extracts large number of electrons enhanced by surface roughness and impurities

• Kilpatrick (1957) has fitted existing data to a formula:

f=1.64E2exp(-8.5/E)

Kilpatrick sparking criterion

Nowadays we can reach fields up to 2 Kilpatrick in CW operation thanks to cleaner vacuum and surface.

We can define a bravery factor b=ES/EK

RF electric breakdown: Kilpatrick criterion f=1.64E2EXP(-8.5/E)

02468

1012141618202224262830

0 100 200 300 400 500 600 700 800 900 1000

frequency [MHz]

Ele

ctri

c fi

eld

[M

V/m

]

Alvarez Drift-Tube Linac (DTL)

Tuning plunger

Quadrupole lens

Drift tube

Cavity shellPost coupler

L=βλ=c/f

Design of a DTL

The fields, power, transit-time factors for the synchronous particle and the shunt impedance calculations are usually done using electromagnetic field-solver codes such as SUPERFISH.

This procedure results in an optimum cell geometry in which the gap length, drift-tube shape and tank diameter are determined.

Then the beam dynamics design is done.

Design of a DTL