Lecture 3, Particle Acceleration - US Particle Accelerator School

51 Pages·2009·1.39 MB·English

LLeeccttuurree 33
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• Electrostatic accelerators
• RRaaddiioo-ffrreeqquueennccyy ((RRFF)) lliinneeaarr aacccceelleerraattoorrss
• RF Cavities and their properties
• Material is covered in Wangler, Chapter 1
(and also in Wiedemann Chapter 15)
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• We can accelerate charged particles:
– eeleecctroonss ((ee-)) aandd ppoossitroonss ((ee+))
– protons (p) and antiprotons (p)
– IIoonnss ((ee.gg. HH1-,NNee2+, AAuu92+, …))
• These particles are typically “born” at low-
eenneerrggyy
– e- : emission from thermionic gun at ~100 kV
– pp//iioonnss:: ssoouurrcceess aatt ~5500 kkVV
• The application usually requires that we
accelleratte tthhese parttiiclles tto hhiighher energy, iin
order to make use of them
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• Lorentz force equation gives the force in response to electric
and magnetic fields:
• The equation of motion becomes:
• The kinetic energy of a charged particle increases by an
amount equal to the work done (Work-Energy Theorem)
r r r r r r
r
ΔW = ∫ F ⋅dl = q∫ E ⋅dl + q∫ (v × B)⋅dl
r r r r r
rr rr
ΔΔWW = q∫∫ EE ⋅ddll + q∫∫ ((v × BB))⋅vddt = q∫∫ EE ⋅ddll
EElleeccttrroommaaggnneettiicc FFoorrcceess oonn CChhaarrggeedd PPaarrttiicclleess
• We therefore reach the important conclusion that
– Magnetic fields cannot be used to change the kinetic
eenneerrggyy ooff aa ppaarrttiiccllee
• We must rely on electric fields for particle
acceleration
– Acceleration occurs along the direction of the electric
field
– EEnneerrggyy ggaaiinn iiss iinnddeeppeennddeenntt ooff tthhee ppaarrttiiccllee vveelloocciittyy
• In accelerators:
– LLoonnggiittuuddiinnaall eelleeccttrriicc ffiieellddss ((aalloonngg tthhee ddiirreeccttiioonn ooff
particle motion) are used for acceleration
– Magnetic fields are used to bend particles for
gguuiiddaannccee aanndd ffooccuussiinngg
AAcccceelleerraattiioonn bbyy SSttaattiicc FFiieellddss::
EEEElllleeeeccccttttrrrroooossssttttaaaattttiiiicccc AAAAcccccccceeeelllleeeerrrraaaattttoooorrrrssss
AAcccceelleerraattiioonn bbyy SSttaattiicc EElleeccttrriicc FFiieellddss
• We can produce an electric field by establishing a potential
difference V between two parallel plate electrodes,
0
separated by a distance L:
LL
E =V / L
z 0
+q
•• AA cchhaarrggeedd ppaarrttiiccllee rreelleeaasseedd ffrroomm
the + electrode acquires an
increase in kinetic energy at the E
– electrode of
+ -
L L
ΔW = ∫ F dz = q∫ E dz = qV
z z 0 V
0 0 0
TThhee SSiimmpplleesstt EElleeccttrroossttaattiicc AAcccceelleerraattoorrss::
EElleeccttrroonn GGuunnss
EElleeccttrroossttaattiicc AAcccceelleerraattoorrss
• Some small accelerators, such
as electron guns for TV picture
tubes, use the parallel plate
geometry just presented
• Electrostatic particle
accelerators generally use a
slightly modified geometry in
which a constant electric field is
produced across an
accellerattiing gap
• Energy gain:
Accelerating
ccoolluummnn iinn
∑
W = nq V
electrostatic
n
accelerator
• LLiimmiitteedd bbyy tthhee ggeenneerraattoorr
∑
V = V
generator n
CCaassccaaddee GGeenneerraattoorrss,, aakkaa CCoocckkrroofftt--WWaallttoonn
AAcccceelleerraattoorrss
Cockroft and Waltons 800 kV
accelerator, Cavendish Laboratory,
Cambridge, 1932
Modern Cockroft-
Waltons are still
They accelerated protons to 800 kV
used as proton
injectors for linear and observed the first artificially
accelerators
produced nuclear reaction:
p+Li →2 He
This work earned them the Nobel Prize
in 1951