mode - CERN Accelerator School

Beam
Synchronism y condition
The distance between accelerating gaps is proportional to particle velocity
Electric field
(tti (at time tt) 0 )
1
0.5
0
0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 z
-0 .5
-1
l=βλ/2
Example: a linac superconducting 4-cell
accelerating structure
Synchronism condition:
t (travel between centers of cells) = T/2
l 1
=
βc
2 f
l
β c
= =
2 = = f
βλ
2
1. In an ion linac cell length has to increase (up to a factor 200 !) and the linac will
be made of a sequence of different accelerating structures (changing cell
length, frequency, operating mode, etc.) matched to the ion velocity.
2. For electron linacs, β =1, l =λ/2 → An electron linac will be made of an injector +
a series i of f id identical ti l accelerating l ti structures, t t with ith cells ll all ll the th same length l th
Note: in the example above, we have synchronism only if we neglect the
increase in beta inside the structure !
4