Download Most simple, linear accelerator

Motivation & History
Rutherford Experiment
one of 1st experiments with „accelerated“ particles
decay of 214𝑃𝑜 → 4𝐻𝑒 2+ @ 7.7 𝑀𝑒𝑉 (6.4% 𝑜𝑓 𝑐) →
197
𝐴𝑢
𝐻𝑒

if Au-nucleus pointlike:
𝐴𝑢
𝑑𝑚𝑖𝑛 = 30 ∙ 10−15 𝑚 = 30 𝑓𝑚
𝑑𝑚𝑖𝑛
 Au-nucleus extended:

3
experiment  Rutherford formular at ≈ 𝑑 = 7.5 𝑓𝑚 ≈ 1.3 ∙ √197
→ result: nucleus almost pointlike, details not „visible“
→ atomic physics opens as new research field
beyond Rutherford
„observe“ with λ ≤ RN
𝜆
small λ → high energy 𝑒 −
𝜆𝑒 − =
ℎ∙𝑐
𝐸
E
λ [fm]
100 MeV
12
1000 𝑀𝑒𝑉 = 1 𝐺𝑒𝑉
1.2
1000 𝐺𝑒𝑉 = 1 𝑇𝑒𝑉
0.0012
𝐴𝑢
for details
nuclear physics
,
𝐸 ≈𝑝∙𝑐
Accelerator needed for physics of (atoms), nuclei, elementary particles, …

Motivation & History
Most simple, linear accelerator
electrostatic, dc voltage
heater
-
e -emission
dc beam
Ring shaped accelerator
bending
magnet
ac voltage, beam from bunches,
(bunched beam)
∆𝑇 =
~𝑈
sin 𝑓𝑡
1
𝑓
f and B-field synchronized
bunches
from electrostatic
injector
curvature „rips off” 𝐸⃑ - field
𝑒−
→ (synchroton) radiation
𝐸
∆𝐸~ 𝑅2 limits achievable e--energy
𝛾4
radiation is new tool for:
𝑅
𝐸 − ∆𝐸
- material science
- nuclear physics
- ...

Motivation & History
Dedicated synchroton radiation machines
goal is radiation, NOT fast electrons
Neutron sources
n
protons @ MeV … GeV
n
target
n
Colliders
E lost for acceleration of centre of mass (c.o.m.)
𝑚1 ∙ 𝑣1
𝑚1 ∙ 𝑣2 = 0
→ lost for physics experiments
𝐸𝑐𝑚 = √2𝑚𝑐 2 ∙ 𝐸1
𝑚, 𝐸

𝑚, 𝐸
𝐸𝑐𝑚 = 2𝐸
Motivation & History
Linear colliders
Circular colliders
(𝑒 − ↔ 𝑒 + )
(𝐴𝑢 ↔ 𝐴𝑢, 𝑝 ↔ 𝑝, 𝑒 ↔ 𝑒)
𝑒−
collisions
𝑒+
building accelerators: challanges in technology:
magnetic fields:
strong, homogeneous in time and space
electric fields:
creation (rf-sources), field breakdown mitigation
beam handling:
low losses, small beams (i.e. repelling forces!)
good 𝑒 − -beam → good photon beam, brilliance!
diagnostic:
beam properties (# particles, E, size, divergence)
machine protection E(LHC) = 780 MJ
improved beam controls:
 material manipulation (holes, implantation)
 medicine, food control, …

Motivation & History
Greinacher Circuit
 grid voltage 𝑈0
 create dc-voltage 𝑈 ≫ 𝑈0
①
𝐶1
②
𝐶3
④
𝑈𝐶1
𝑈(𝑡)
𝐷1
𝐷2
𝐷3
𝐶2
③
𝑈(𝑡)
simplified model
𝑈
1
3
𝑡
2𝜋
(4𝜔)
5
−𝑈
𝑈0
2𝑈0
2𝑈0

4𝑈0
4𝑈0
Motivation & History
t
𝑡
<2
2𝜋
(4𝜔)
simple model
① @ − 𝑈0
② @ 0𝑉
𝑈(𝐶1 ) = ② − ① = 0 + 𝑈0
2≤
𝑡
<4
2𝜋
(4𝜔)
① @ + 𝑈0
𝑈(𝐶1 ) = 𝑈0 → ② @ 2𝑈0 w.r.t. ground
② cannot "discharge" because its 𝛥𝑉 w.r.t. ground closes 𝐷1
4≤
𝑡
<6
2𝜋
(4𝜔)
⋮
① @ − 𝑈0
𝑈(𝐶1 ) = 𝑈0 → ② @ 0𝑉 again
𝐷1 remains always closed → 𝐶1 keeps always 𝑈0 ,
② 𝑈0 higher than ①
𝐶2 charged through 𝐶1 to 2𝑈0
t with ② @ 2𝑈0
③ @ 2𝑈0
𝑈(𝐶3 ) = 2𝑈0
④ @ 4𝑈0 = 2𝑈0 [② − ①] ] + 2𝑈0 [④ − ②]
𝑈(𝐶2 ) = 2𝑈0 , since 𝐷2 forbids discharge
t with ② @ 0𝑉
③ @ 2𝑈0
④ @ 2𝑈0

Motivation & History
Real process
 charging of 𝐶𝑠 in steps
 charging of 𝐶2 will discharge 𝐶1
 all 𝐶𝑠 recharged by grid
Dc-Accelerator of Cockcroft & Walton
source
𝐸⃑
acceleration
tubes
collector, target

Motivation & History
 𝑈𝑚𝑎𝑥 = 4 𝑀𝑉 achieved
 𝐼𝑚𝑎𝑥 = 100 𝑚𝐴 (protons)
(≈ 𝜇𝑠 pulses)

7
𝐿𝑖 + 𝑝 → 2 4𝐻𝑒 observed
Van-der-Graaf Generator
𝐸=0
𝐼 ≈ 𝜇𝐴, 𝑑𝑐
≤ 16 MW

Motivation & History
Tandem
negative ions
foil
target
positive ions
use voltage twice!
First terms
Energy per nucleon 𝐸𝑢 =
𝑡𝑜𝑡𝑎𝑙 𝑘𝑖𝑛.𝑖𝑜𝑛 𝑒𝑛𝑒𝑟𝑔𝑦
𝑖𝑜𝑛 𝑚𝑎𝑠𝑠 𝑛𝑢𝑚𝑏𝑒𝑟
𝐴 𝑞+
𝑋
𝑞
𝐸𝑢 = 𝐴 ⋅ 𝑒 ⋅ 𝑈 [𝑀𝑒𝑉⁄𝑢]
Eu defines velocity
𝛾 =1+
=
𝐸𝑢
𝐸𝑢 [𝑀𝑒𝑣 ⁄𝑢]
=1+
𝑚𝑢
939.487 𝑀𝑒𝑣⁄𝑢
1
√1−𝛽2
→ 𝛽 = √1 − 1⁄𝛾 2
𝛽 ∙ 𝛾 = √𝛾 2 − 1

Motivation & History
Beam rigidity (Bρ)
𝑣
𝐵𝜌 ∶= magn.field ∙ curvature radius
AXq+
𝑒∙𝑞∙𝑣∙𝐵 =
R
𝐴∙𝑚𝑢 ∙𝛾∙𝑣 2
𝑅
𝐵 ∙ 𝑅 ∶= 𝐵𝜌 =
B
=
𝐵𝜌 = 3.1071 𝑇𝑚 ∙ 𝑞 ∙ 𝛽 ∙ 𝛾
electrons:
𝐵𝜌 = 1.705 ∙ 10−3 𝑇𝑚 ∙ 𝛽 ∙ 𝛾
𝑑𝛽
= 𝛾 3 ∙ 𝛽,

𝑒∙𝑞
𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚
𝑐ℎ𝑎𝑟𝑔𝑒
𝐴
ions:
𝑑𝛾
𝐴∙𝑚𝑢 ∙𝛾∙𝑣
𝜕𝛾 = 𝛾 ∙ 𝛽 2 ∙
𝜕𝑝
𝑝
,
𝜕𝑝
𝑝
=
𝛾
𝜕𝐸𝑘
𝛾+1 𝐸𝑘
,
𝜕𝑝
𝜕𝛽
= 𝐴 ∙ 𝑚𝑢 ∙ 𝛾 3 ∙ 𝑐