10
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N
S S N
N S
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● 1939: Lawrence uses 60’ cyclotron for 9MeV protons, 19MeV deuterons, and 35MeV 4He. First tests of tumor therapy with neutrons via d + t ! n + α With 200-800keV d to get 10MeV neutrons.
First Medical Applications
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The Loma Linda proton therapy facility
Modern Nuclear Therapy
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● Electrons are quickly relativistic and cannot be accelerated in a cyclotron. ● In a microtron the revolution frequency changes, but each electron misses an integer number of RF waves.
● Today: Used for medical applications with one magnet and 20MeV. ● Nuclear physics: MAMI designed for 820MeV as race track microtron.
The microtron
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● The extra time that each turn takes must be a multiple of the RF period.
qBp
=ρ
KqBc
mmqB
vvt
nn
n
n
n
n
Δ=−=
−=Δ
+
+
+
2010
1
1
2)(2
)(2
πγγ
π
ρρπ
RF
qBcnKω
2
=Δ for an integer n B=1T, n=1, and fRF=3GHz leads to 4.78MeV This requires a small linear accelerator.
qBp
pdpvdt
ddlqvB
dtdp
===⇒=/ϕ
ρ
ϕpddp =p
ϕd
The microtron condition
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Wideroe
non-relativistic:
221
0max sin nn mvnqUK == ψ
nTvl RFnRFnn ∝== λβ21
21
Called the π or the 1/2βλ mode
(Faraday cage)
+ + + + - - - -
Wideroe linear accelerator
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π or the 1/2βλ mode
● 1933: J.W. Beams uses resonant cavities for acceleration
Traveling wave cavity:
Standing wave cavity:
)sin(),( max kstEstE −≈ ω
)sin()sin(),( max kstEstE ω≈
particlephase vk
v ==ω
Transit factor (for this example): max21
0
),(1particle
EdssEERF
vs
RF
≈= ∫λ
λ
particlevk=
ω
)(sin),( 2maxparticle
ksEsE vs ≈
Here v=c for electrons
Accelerating cavities
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2π or the βλ mode
- - - - - + + + + +
Needs only one power input coupler and walls do not dissipate energy.
+ + + + + + + + + - - - - - - - - -
The Alvarez Linear Accelerator
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