Particle Accelerators - CERN Summer Student Program [lectures]

107 Pages·1996·2.44 MB·English

by  J. Jowett

Particle Accelerators
Lecture 1:
Introduction,
Types of Accelerator,
Limits on Energy
John Jowett
(ex-Summer Student)
SPS-LEP Division, CERN
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Overview of this course
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Principles of Particle Acceleration
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Linear Accelerators
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Energy Limits for Circular Accelerators
J.M. Jowett Particle Accelerators, Lecture 1, Page 1
Overview of Course
“A selective introduction to the physics and
engineering of the particle accelerators that
make experimental particle physics possible.”
1. Introduction, types of accelerator, ultimate limits
Today’s introduction, physical phenomena which limit
energy
2. Beam dynamics in modern synchrotrons and
storage rings
Some basic principles and theory of acceleration and
focusing
3. Sub-systems of a large accelerator
Hardware: magnets, accelerating systems, vacuum
systems, engineering, instrumentation, ...
4. Application to the LEP collider
LEP as an example, in some detail. Effects of synchrotron
radiation. Luminosity.
5. (If time available: Special topic: Spin-polarized
beams.)
J.M. Jowett Particle Accelerators, Lecture 1, Page 2
Suggested Reading
&
M. Sands, The Physics of Electron Storage Rings, SLAC-121
(1970).
Probably unsurpassed in clarity for basic single particle dynamics and effects of
synchrotron radiation. [Some copies available from J. Thomashausen, SL
Division, <[e-mail]>]
&
H. Wiedemann, Particle Accelerator Physics, Springer-Verlag,
Berlin, 1993.
Comprehensive modern introduction in first volume, Vol II is more advanced.
&
M. Reiser, Theory and Design of Charged Particle Beams,
Wiley, New York 1994.
Comprehensive advanced text including high current accelerators, particle
sources, etc.
&
CERN Accelerator School, Fifth General Accelerator Physics
Course, Ed. S. Turner, CERN Report 94–01 (1994).
See also previous schools in this series, including more advanced and
specialised schools.
&
US Particle Accelerator School, AIP Conference Proceedings,
Nos. 87, 153, 184, ....
&
A.W. Chao, Physics of Collective Beam Instabilities in High
Energy Accelerators, Wiley, New York 1993.
Covers collective effects at fairly advanced level.
&
L. Michelotti, Intermediate Classical Dynamics with
Applications to Beam Physics, Wiley, New York 1995.
Mathematically-oriented modern dynamics text with accelerator applications.
&
J.D. Jackson, Classical Electrodynamics, Wiley, New York
1975.
Classic text on electrodynamics, includes relativistic dynamics and treatments of
radiation from accelerated charges.
J.M. Jowett Particle Accelerators, Lecture 1, Page 3
Other Sources of Information
about Particle Accelerators
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World-Wide-Web
CERN Home Page leads to many places:
http://www.cern.ch/
My own little collection:
http://hpariel.cern.ch/jowett/accelerator.html
A more comprehensive list at Los Alamos:
http://www.atdiv.lanl.gov/doc/laacg/codehome.html
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CERN Accelerator School
“basic and advanced two-week courses on general
accelerator physics aiming to bridge the gap between ... a
science or engineering degree and ... accelerator research
work.” Varying locations.
http://www.cern.ch/Schools/CAS/
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US Particle Accelerator School
Courses give credit in US universities:
http://www.fnal.gov/uspas.html
J.M. Jowett Particle Accelerators, Lecture 1, Page 4
Particle in Electromagnetic Field
(No other forces are practical, yet!)
v = pc2 / E, E2 - p2c2= m2c4
E is particle energy
dp E is electric field
= ( + · )
Ze E v B ,
dt
¶
A
= (cid:209)-F - = (cid:209) ·
E , B A
¶
t
dE
(cid:222) = (cid:215) Only longitudinal electric fields
ZeE v
dt
can increase energy!
-(cid:209)F (cid:222)
electrostatic fields (limited utility)
¶ ¶
A B
- (cid:222) (cid:209) · = -
time - varying electric field, E
¶ ¶
t t
q
Waves in free space have purely transverse fields.
Need to impose boundary conditions - a structure.
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All high-energy accelerators use time-dependent electric
fields to increase energy.
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Many use static magnetic fields for bending (purely
transverse acceleration)
For simplicity we will mostly consider the case Z=1.
Generally work in the “laboratory” frame.
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We considered one particle in an external field.
Neglect individual and collective interaction between
particles in beam.
J.M. Jowett Particle Accelerators, Lecture 1, Page 5
Linear Accelerators
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Acceleration along a straight line by oscillating
radio-frequency (RF) fields.
C
dA
¶ Stokes Theorem
B d
(cid:209) · = - (cid:219) (cid:215) =(cid:242) - (cid:215) (cid:242)
E E ds B dA
¶
t dt
C A
(cid:222)
Changing magnetic flux Electric field around it
(cid:222)
Higher frequency stronger fields ?
Typical field in resonant cavity E(s,t) = E ei(w t- ks)
0
L L
(cid:242) (cid:242)
D = (cid:215) = (cid:215)
accelerates and decelerates in E E v dt E ds
0 0
(cid:222)
need to arrange that particle only sees field when
(cid:215) >
accelerating, i.e., E v 0
(cid:222)
phase relationships between field and passage of beam
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Acceleration by means of RF fields requires
conditions of synchronism between accelerating
field and the beam.
J.M. Jowett Particle Accelerators, Lecture 1, Page 6
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Example: the Alvarez linac
Beam path is enclosed in conducting drift tubes which shield
particles from the external RF fields, except in the gaps where a
suitable condition of synchronism applies.
Beam
v
RF generator
l
RF
c
1 v
< = l
Drift tube length L 1 vT
2 RF RF
2 c
L increases with velocity of particles.
(Old) Linac1 at CERN: 50 MeV
Alvarez linac (1946)
Alvarez linac (1946)
protons for PS, 29m, 200 MHz
remains very useful as
remains very useful as
pre-accelerator for
pre-accelerator for
most proton
most proton
synchrotrons
synchrotrons
Drift tubes
(usually follows a
(usually follows a
Cockroft-Walton
Cockroft-Walton
electrostatic
electrostatic
accelerator or, Accelerating
accelerator or,
gaps
nowadays, an RF
nowadays, an RF
quadrupole).
quadrupole).
Beam
J.M. Jowett Particle Accelerators, Lecture 1, Page 7
Waveguides
Simplest case of circular pipe, radius a, but main conclusions
valid for elliptial or rectangular cross sections too.
Electric field satisfies wave
s
eqn:
(cid:230) 1 ¶ 2 (cid:246) q
(cid:231) (cid:209) -2 (cid:247) E(r,t) = 0
Ł c2 ¶ t2 ł
r
a
= q
r (r, ,s)
Want solutions for longitudinal
field of form E (r,t)= E (r)einq eiw( t- ks)
s 0n
periodic
= w
Wave of phase velocity v / k, k to be determined
p
Equation for radial dependence
¶ 2E (r) 1 ¶ E (r) (cid:230) w 2 n2 (cid:246)
0n + 0n + (cid:231) - k2- (cid:247) E (r) = 0
¶ r2 r ¶ r Ł c2 r2 ł 0n
( ) ( )
( ) = +
with solutions E r AJ k r BY k r
0n n c n c
w 2 ( )= ¥
Unphysical as Y 0
where k = - k 2 n
c c2
w,
For varying values of n, etc. there are many possible
modes of field oscillations (see, e.g., Jackson). Two
main classes:
TE (transverse electric) all E fields transverse
TM (transverse magnetic) all H fields transverse
J.M. Jowett Particle Accelerators, Lecture 1, Page 8
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Boundary conditions
(cid:222)
Perfectly conducting surface no tangential E
( )
(cid:222) (=) (cid:222) =
E a 0 J k a 0
0n n c
( )
J k r
Radial modes (Bessel functions)
0 c
1
non-zero on axis
0.8 ( )
J k r
1 c ( )
0.6 J k r
2 c ( )
J k r
0.4 3 c
0.2
k r
1 2 3 4 5 6 7 c
-0.2
First zero
=
-0.4 k r 2.405
c
Determines relation of tube radius to minimum
frequency of propagating waves:
w 2 2.405c
= k + k2 where w = ck = is the cutoff frequency
c2 c c c a
of the waveguide.
=
a 0.1 m
w
c
= = >
Phase velocity v c (cid:222) = w »
f 1.1 GHz
p k 1- w 2w / 2 c c
c
dw c2
= = <
Group velocity v c
g
dk v
p
hw
m = c
Photons have positive mass in guide.
g
c2
J.M. Jowett Particle Accelerators, Lecture 1, Page 9
Lowest mode with longitudinal electric field on axis:
( ) 2.405
E (r,t) = E J k r ei(w t- kw ( )s), where k =
s 00 0 c c
a
Azimuthal magnetic field
w
( )
H (r,t) = - i E J k r ei(w t- kw ( )s)
q 00 1 c
ck
c
w
=
E
r
k
Partial success in creating accelerating
Partial success in creating accelerating
electric field: field is longitudinal but
electric field: field is longitudinal but
no particle can stay in step with a wave
no particle can stay in step with a wave
with phase velocity > c.
with phase velocity > c.
q
Need to modify (“load”) the structure to reduce phase
velocity.
N
Exercise: Check the steps and/or read up in Jackson.
{
Exercise: Calculate the mass of a photon in a typical
waveguide. Express in eV and in kg.
J.M. Jowett Particle Accelerators, Lecture 1, Page 10