2. accelerator basics and types - paul scherrer institute · andreas streun, psi 23 2. accelerator...
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Andreas Streun, PSI 23
2. Accelerator basics and types
u Particle sources
u Electric and magnetic fields
u Electrostatic accelerators
n Marx n Cockcroft-Walton n van der Graaff
u Radio-frequency acceleration
u Linear accelerators
n Linac n Buncher n Linear collider n FEL
u Recirculation 1: fixed magnetic field and variable orbit
n Recirculated linac n Microtron n Cyclotron n FFAG
u Recirculation 2: variable magnetic field and fixed orbit
n Betatron n Synchrotron and storage ring
n Light sources n Circular colliders n The LHC
Andreas Streun, PSI 24
Particle sources
® I. Electron sources
n thermionic cathode
n laser cathode (photo effect)
n field emission
Ç gated field emitter (MIT)
field emitter array ð
with a damage
Andreas Streun, PSI 25
Particle sources ® II. Proton [ion] sources
n plasma ion source
n laser ion source
n electron beam
ion source
~p = ~F = q (~v × ~B + ~E), ~v =~p
m
p > 0
p =d
dt
√
~p · ~p =~p · ~pp
=q
p· ~p · (~v × ~B)
︸ ︷︷ ︸⊥~p
︸ ︷︷ ︸=0
+q
p· ~p · ~E
=⇒
p = qE {~p; ~E}
q ~v × ~B = ~F = ~p = m~v m = 0
~B = Bz ~ez −→ vx =q
mvyBz vy = − q
mvxBz vz = 0
=⇒ d/dt . . .
vx(t) = vxo (ωt) + vyo (ωt)vy(t) = vyo (ωt)− vxo (ωt) ω = q
mBz
vz(t) = vzo
=⇒ vzo = 0
x(t) = xo + ρ (ωt− φ) ρ =m√
v2xo+v
2yo
qBz
y(t) = yo + ρ (ωt− φ)z(t) = zo + vzot φ =
vyo
vxo
~B ⊥ ~v ‖ ~E → F = q(vB + E)v → c → F ≈ q(cB + E) [1 e− v = 0.86c]
E ≈ 107 10
B ≈ 2 /10
−→ cB ≈ 100× E
=⇒=⇒
t = 0
T → T + qUo φ
t < 0 t > 0
T → T + qUo (φ + ωt) ≈ T + qUo φ + ωqUo φ · t |t| ≪ τ
0 < φ < π/2 → φ > 0
−→−→
=⇒ [t , t ] =
=⇒
τ = 2π/ω vτv→c−→ λ
v
Ln = τ2vn vn =
√2Tnmo
Tn = nUo φ
Tn = Tn−1 + Uo (φ + ωtn−1)vn =
√
2Tn/mo
tn = tn−1 + Ln(vn − vn)
Uo = 0.1 τ = 1 mo = 1
to = (−0.1 . . .+0.1)τ
φ → π/2
Andreas Streun, PSI 44
Linear colliders why ?
w e+e- collisions complementary to pp (LHC)
w energy limited for circular e+e- colliders (LEP)
ð ILC (International Linear Collider): Ecm = 500 GeV, 31 km
ð CLIC (Compact LInear Collider): Ecm = 3 TeV, < 50 km
Costs become main design criterion.
Linear accelerators
CLIC
ILC
Andreas Streun, PSI 45
Free electron laser
prepare electron beam of very high phase space density:
low transverse emittances, very short pulse, low energy spread
ð coherent emission of light and self amplification (ð ch.6)
1 Å X-ray pulses: pulse length < 100 fs, power > 10 GW
In operation: LCLS (SLAC/USA),
FLASH (DESY/DE)
SACLA (RIKEN/JP)
Under construction: XFEL (DESY/EU)
SwissFEL (PSI/CH)
ð Linac development is common PP and MR interest
LCLS undulator line
Linear accelerators
β → 1
k tk = 2πRk+2Lc
Rk
mv2
R= evB
v≈c−→ Rk = moγkc
eB= Ek
eBc−→ tk = 2πEk
eBc2+ 2L
c
∆t = tk+1 − tk = 2πeBc2
(Ek+1 − Ek)︸ ︷︷ ︸
=∆E
!= nτ
∆E/e × f = 14.3 nB
⇐= =⇒
~E = − ~B
B ~B = B(r, t)~ez∮~E(t) · ~eφ ds = −
∫ ∫~B(r, t) · ~ez rdrdφ
2πRE(t) = −〈 ~B(t)〉πR2 → E = Eφ = −12R〈B〉
mv = p = eRB(r=R)
p = F = eE = 12eR〈B〉
=⇒
B = 12〈B〉 B(t) = 1
2〈B(r, t)〉 +Bo
R BodB(r)dr|R
mv2
R= qvB −→ p = qRB −→ p(t) = qRB(t)
• Bo po = qRBo
• B −→ B +∆B
• ∆R < 0
• 2π∆R
• ∆t = 2πβc∆R < 0
• U (∆t) = qUo (ω∆t + φ) > 0∆t < 0 φ ≈ π
• ∆p = βqU (∆t)
=⇒ p(t) B(t)
φ ≈ π 2πR = nβλ
• B p = qRB
−→ −→
∆E = qUo φ−∆E = 0.∗)
∗)
P = 88.5(E )4 × I
R
E =I =R =
E = 100 I ≈ 2× 5
B = 0.11 → R = 3 ≈ 70 → 27
≈ 30 > 60
=⇒ −→