Download Particles Accelerated in Straight Line Electrostatic or RF

Accelerator Physics
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Basic Formalism
Linear Accelerators
Circular Accelerators
Magnets
Beam Optics
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Greg LeBlanc
Lead Accelerator Physicist
Australian Synchrotron Project
Basic Formalism
Lorentz Force
F  qE  v  B 
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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  E0  Ekin
 Rest Energy:
E0  m0 c 2
 Relativistic Parameter:   E E
0
 Velocity:
  c
 Relativistic Mass:
m
 Energy in eV:
1eV  0.16 10 18 J
m0
1 
2
 m0
(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
0.5


0.6
0.4
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
0.5
1
1.5
0
1
2
2
3
2.5
3
E [MeV]
4
5
E [GeV]
3.5
6
4
7
8
4.5
9
5
10
5.5
Linear Accelerators
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Particles Accelerated in Straight Line
Electrostatic or RF Fields
i t  ks 


E


E

e
Planar Wave
0
 k 0
Static Case
d
Lorentz Force F  dt m0c  qE  
Energy Gain
Ekin  q  E  ds
Lcy
Linear Accelerators
Electrostatic Accelerators
 Electron Gun
 Van de Graaff generator (~20MV)
Linear Accelerators
RF Accelerators
 Wideroe
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Long for low frequency
Losses
 Alvarez
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Higher frequency
Higher voltages
Li 
1
v i Trf
2
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  10 8 m / s; Trf  1 / 3  10 9 s  5cm
2
Circular Accelerators
 Circular Motion in a Magnetic
Field
2

Centripetal Force
Lorentz Force

B, r or T constant

mv
F
r
F  qvB
mv
r
qB
rqB
v
m
2r 2m
T

v
qB
Circular Accelerators
 Cyclotron
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Constant B
Non-relativistic
2m0
T
qB
Circular Accelerators
 Microtron
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Synchronicity for
=integer
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Ee=n x 511 keV

Ep=n x 938 MeV
 Race Track Microtron
Circular Accelerators
 Synchrotron
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Constant r and T
Magnets ‘Ramped’
Storage Ring
Magnets
Dipoles for Steering
 Magnetic Field
nI 0
B
h
Magnets
Quadrupoles for Focusing
 Gradient
2 0 nI
g
R2
Magnets
 Sextupoles
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Chromatic effects
 Octupoles
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Correcting Magnetic Errors
Beam Optics
Coordinate System
 Curvilinear System
 Motion Relative Ideal Path
individual particle trajectory
s
y
S
ideal path
y
x
x
r
Beam Optics
-4
6
4
2
0
x [m]
 Particle motion
determined by
magnetic lattice
 Studied using
simulation
software
Particle Trajectories
x 10
-2
-4
-6
0
2
4
6
8
S [m]
10
12
14
16
Beam Optics
 Machine
Functions
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Beam Motion
Beam Size
Beam
Emittance
x
y
30
10*x
25
20
15
[m]
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Machine Functions
35
10
5
0
-5
0
2
4
6
8
S [m]
10
12
14
16
Beam Optics
Measured Response Matrix
 Response Matrix

Probe the Machine with
the Beam
Calibrate Models
1
0.5
[mm]

0
-0.5
-1
46
35
46
35
24
24
13
13
2
2
45
45
34
34
23
23
12
HCM# and VCM#
1
12
1
HBPM# and VBPM#
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