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

=⇒=⇒

< −→

=⇒ =⇒

Un = nUo

••••U ∼ 6

Un(t) = 2nUo

+Uo (ωt)

••U ∼ 4

=

U ∼ 10

=⇒H− → H+

U ∼ 10

=⇒ T = qU < 10

q = ±e

|q/e| > 1 −→

W±, Z,H◦ > 100

= . . .

v ≪ c Ln = τ2v = τ

2

√2Tmo

= τ2

√2nqUo φ

mo

U = Uo (ωt + φ) −→ T = nqUo[ φ]

φ φ = π2

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

!=

R

∆z

⊲ v ≪ c⊲ ∼ 100⊲ 1 . . . 10

⊲ v ≈ c⊲ ∼ 3⊲ µ 10 . . . 100⊲ 10 . . .

⊲−→

⊲ ∼ 100 . . . 3⊲ ∼ 1

φ ≈ 0 → ∆T = qU (ω∆t) ≈ ωqU∆t

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

∆ta→a!= nτ n ∈ N

> ∆Ta→a→b

−→

130 2×

6 5×

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

3.5 −→ 14 −→ 180 −→ 850 −→ 1.5

850 n = 1, f = 2.5 , B = 1.3 , ∆E = 7.5

β ≪ 1

mov2

R= evB −→ t = 2πR

v= 2πmo

eB

t β ≪ 1 −→

ωc =2πt= e

moB ω

!= nωc

←80≈ 15

→

70

590

2=⇒ > 1

⇐= =⇒

~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

=⇒ −→

• ↔ • E E

2n2× n• = • E = E

1 2n > 2n

• 6= • E 6= E

1

• = • E = E

•

⊲ →⊲ →

•

⊲

•

⊲

⊲

•

⊲

⊲ e+ ↔ e− p↔ p

⊲ Φ

⊲ e− ↔ p + ↔ + µ+ ↔ µ−

0.65 π

8 1436

2.4 288

←

e+e−

→

e−e−

× ppւ

†× pp

=

Φ × e+e−

e− ↔ e+

e− ↔ e+

Z →

ց

↓

26′658.883

123212 1.9

∼450

≈ 15E = 450→ 7000B = 0.535→ 8.33

=⇒ ⋆⇐=∼

=⇒

=⇒

3500

6500