# Accelerator Physics

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```					               Accelerator Physics

   Basic Formalism
   Linear Accelerators
   Circular Accelerators
   Magnets
   Beam Optics
   Our Accelerator

Greg LeBlanc
Australian Synchrotron Project
Basic Formalism

Lorentz Force
F  q E  v  B 

 Only works on charged particles
 Electric Fields for Acceleration
 Magnetic Fields for Steering
 Magnetic fields act perpendicular to the direction of
motion.
 For a relativistic particle, the force from a 1 Tessla
magnetic field corresponds to an Electric field of 300
MV/m
Basic Formalism

Energy
E  E 0  E kin
 Rest Energy:              E0  m0 c 2
 Relativistic Parameter:   E E
0

 Velocity:                   c
m0
 Relativistic Mass:        m                 m0
1    2

 Energy in eV:             1eV  0.16 1018 J
(Electron rest mass 9.1*10 -31kg gives a rest energy of 511 keV)
Basic Formalism
 Particles Relativistic when 1
Electrons
1

0.9                                                                   Protons
1

0.8                             0.9

0.7                             0.8

0.7
0.6
0.6

0.5


0.5


0.4                             0.4

0.3
0.3

0.2
0.2
0.1

0.1
0
0       1      2     3    4        5      6   7         8   9   10
E [GeV]
0
0    0.5   1    1.5                 2       2.5       3       3.5         4       4.5       5    5.5
E [MeV]
Linear Accelerators

   Particles Accelerated in Straight Line
   Electrostatic or RF Fields
   Planar Wave       E    E0  e i t  ks 
 k 0
   Static Case
F  m0c  qE  
d
   Lorentz Force          dt
   Energy Gain       Ekin  q  E  ds
Lcy
Linear Accelerators

Electrostatic Accelerators

 Electron Gun

 Van de Graaff generator (~20MV)
Linear Accelerators

RF Accelerators
 Wideroe
   Long for low frequency
1
   Losses                        Li      vi Trf
2

 Alvarez
   Higher frequency
   Higher voltages
Linear Accelerators

 Travelling Wave

 Standing Wave
Synchronicity in a LINAC

The length of the ith drift tube is
1
Li  iTrf
2
where  i is the velocity of the particles in the ith drift
tube and Trf is the rf period.
Australian Synchrotron Example:
Electrons at the speed of light (a valid approximation
above 5 MeV) in a 3 GHz linac
1
                                
L  cTrf  c  3  108 m / s; Trf  1 / 3  109 s  5cm
2
Circular Accelerators

 Circular Motion in a Magnetic Field
2
mv
   Centripetal Force    F
r
   Lorentz Force        F  qvB
mv
r
qB
rqB
v
m
2r 2m
   B, r or T constant   T     
v   qB
Circular Accelerators

 Cyclotron
   Constant B
   Non-relativistic

2m0 
T
qB
Circular Accelerators

 Microtron
   Synchronicity for

=integer

   Ee=n x 511 keV

   Ep=n x 938 MeV

 Race Track Microtron
Circular Accelerators

 Synchrotron
   Constant r and T
   Magnets ‘Ramped’
   Storage Ring
Magnets

Dipoles for Steering

 Magnetic Field
nI 0
B
h
Magnets

2 0 nI
g
R2
Magnets

 Sextupoles
   Chromatic effects
 Octupoles
   Correcting Magnetic Errors
Beam Optics

Coordinate System
 Curvilinear System                   individual particle trajectory
y       s
 Motion Relative Ideal Path
S
ideal path
x             y

x                 r
Beam Optics
-4
x 10                 Particle Trajectories
6

 Particle motion            4

determined by              2

magnetic lattice
0

 Studied using
x [m]

simulation                 -2

software                   -4

-6

0        2   4   6            8              10   12   14   16
S [m]
Beam Optics

 Machine                  35
Machine Functions

x
y
Functions                30
10*x

25
   Beam Motion
20

   Beam Size
15

Beam
[m]


10

Emittance            5

0

-5

0   2   4   6          8            10   12   14           16
S [m]
Beam Optics
Measured Response Matrix

 Response Matrix
   Probe the Machine with
the Beam
1

   Calibrate Models       0.5

0
[mm]

-0.5

-1

46
35                                                                                        46
24                                                                              35
13                                                                    24
2                                                           13
45                                                  2
45
34                                   34
23                       23
12            12
HCM# and VCM#                          1    1                    HBPM# and VBPM#
Our Accelerator
Our Accelerator
Our Accelerator
Our Accelerator
Our Accelerator
Our Accelerator

```
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