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DB Injector Thermionic gun 2.1.

Thermionic & RF Gun Simulations
for the CLIC DB Injector
Mohsen Dayyani Kelisani
1. Institute For Research in Fundamental Science (IPM), Tehran, Iran
2. CERN, Geneva, Switzerland
Contents
1. Introduction
1.1. CLIC DB Injector Layout
1.1. Basic Beam Dynamics Studies (Emittance Growth)
2. DB Injector Thermionic gun
2.1. Thermionic Gun Design
2.2. Thermionic Gun Simulations
3. DB injector RF gun
3.1. RF Gun Design
3.2. RF Gun Simulations
3.3. Comparison
1. Introduction
DC Gun
1
1.1. CLIC DB Injector Layout (2 Options)
Bunching System
RF Gun
13 TW Accelerating Structures
12 TW Accelerating Structures
1. Introduction
2
1.2. Beam Dynamics Studies (Emittance Growth)
Wangler’s formula:
Any non-uniformity in the beam
distribution will result in the
emittance growth specially in
nonrelativistic beams and beams
with bigger RMS radiuses
π‘‘πœ–π‘› 2
𝑑𝑧
=
𝑒𝑐𝑅 2
𝑑
βˆ’
βˆ†π‘ˆ
2πΌπ‘šπ‘ 2 𝛾2 βˆ’1 𝑑𝑧
Gamma Energy
πœ€π‘› =
RMS beam radius
Potential Energy difference
Between the beam and its
equivalent uniform beam
π‘₯ 2 𝛾𝛽π‘₯ β€² 2 βˆ’ π‘₯𝛾𝛽π‘₯ β€²
Nonlinear fields change the
beam uniformity and cause
to emittance growth
2
1. Introduction
3
1.2. Beam Dynamics Studies (Designing Strategies)
Wangler’s formula:
π‘‘πœ–π‘› 2
𝑑𝑧
Strategies for designing a
low emittance electron gun
=βˆ’
πœ‹πœ€0 𝑒𝑐𝑅 2
𝑑
βˆ†π‘ˆ
2πΌπ‘šπ‘ 2 𝛾2 βˆ’1 𝑑𝑧
1) Design the gun with as
much as possible linear
electromagnetic fields
2) Minimize the action of
remaining nonlinearities
with faster acceleration
and smaller beam size
2. DB Injector Thermionic Gun
4
2.1. Thermionic Gun Design (Potential Expansion)
∞
βˆ’1
𝑉 π‘Ÿ, 𝑧 = 1 +
𝑛=1
According to the Maxwell
equations for axisymmetric
electrostatic fields we can
write:
𝐸𝑧 π‘Ÿ, 𝑧 = βˆ’ 1 +
πΈπ‘Ÿ π‘Ÿ, 𝑧 =
𝑛
π‘Ÿ
2
𝑛!
2
2𝑛
𝑑 2𝑛
𝑉 𝑧
𝑑𝑧 2𝑛
π‘Ÿ
βˆ’1 𝑛 2
∞
𝑛=0
𝑛! 2
π‘Ÿ
× 1+
2
∞
𝑛=1
2𝑛
𝑑2𝑛
𝑑𝑧 2𝑛
𝑉′ 𝑧
π‘Ÿ 2𝑛 2𝑛
βˆ’1
𝑑
2
𝑛! 𝑛 + 1 ! 𝑑𝑧 2𝑛
𝑛
𝑉 β€²β€² 𝑧
If we can somehow find the potential function on symmetric axis z then we
can easily find the electrostatic potential every where and so the electrode
shapes
If we want to have a linear electrostatic field we should have a parabola
shape for potential function on symmetric axis
2. DB Injector Thermionic Gun
5
2.1. Thermionic Gun Design (Envelope Equation)
Envelope equation:
β€²
β€²β€²
𝛾
×
𝛾
𝛾
×
𝛾
𝑅′′ + 2
× π‘…β€² +
𝛾 βˆ’1
2 𝛾2 βˆ’ 1
π‘žπΌ
×𝑅 =
4πœ‹πœ–0 π‘π‘šπ‘ 2 𝛾 2 βˆ’ 1
4πœ€π‘› 2
+ 3 2
3/2 𝑅
𝑅 𝛾 βˆ’1
+
π‘ž
𝛾 𝑧 =1+
𝑉
βˆ’ 𝑉 𝑧
π‘šπ‘ 2 π‘π‘Žπ‘‘β„Žπ‘œπ‘‘π‘’
β€²
2
β€²β€²
2 βˆ’ 1πœ€ 2
2𝑅
2π‘šπ‘
4
𝛾
π‘žπΌ
𝑅
𝑛
𝑉 β€²β€² +
𝑉′ = βˆ’
+
βˆ’
𝛾2 βˆ’ 1
4
𝑅
π‘žπ›Ύ
𝑅
4πœ‹πœ–0 π‘π‘šπ‘ 2 𝑅2 𝛾 2 βˆ’ 1 𝑅
2. DB Injector Thermionic Gun
6
2.1. Thermionic Gun Design (Potential Equation)
2𝑅 β€² β€²
2π‘šπ‘ 2 4 𝛾 2 βˆ’ 1πœ€π‘› 2
π‘žπΌ
𝑅 β€²β€² 2
𝑉 +
𝑉 =βˆ’
+
βˆ’
𝛾 βˆ’1
𝑅
π‘žπ›Ύ
𝑅4
4πœ‹πœ–0 π‘π‘šπ‘ 2 𝑅 2 𝛾 2 βˆ’ 1 𝑅
β€²β€²
𝑉𝑐 = 140 π‘˜π‘‰
Very close to a
parabola and
so linear fields
𝑑 = 51.6π‘šπ‘š
2. DB Injector Thermionic Gun
7
2.1. Thermionic Gun Design (Equipotential Surfaces)
𝑉 π‘Ÿ, 𝑧 =
∞
1+
βˆ’1
𝑛=1
𝑛
π‘Ÿ
2
𝑛!
2
2𝑛
𝑑 2𝑛
𝑉 𝑧
𝑑𝑧 2𝑛
𝑉 π‘Ÿ, 𝑧 =0 kV
Anode
𝑉 π‘Ÿ, 𝑧 =140kV
Cathode
2. DB Injector Thermionic Gun
8
2.1. Thermionic Gun Design (Cathode Shape)
A parabola could be a
good approximation
for the cathode shape
2. DB Injector Thermionic Gun
9
2.1. Thermionic Gun Design (Anode Shape)
A nose could be a
good approximation
for the anode shape
2. DB Injector Thermionic Gun
10
2.1. Thermionic Gun Design (DC Gun Geometry)
𝑉 = βˆ’140π‘˜π‘‰
𝑉 = 0π‘˜π‘‰
πΆπ‘Žπ‘‘β„Žπ‘œπ‘‘π‘’ π‘Ÿπ‘Žπ‘‘π‘’π‘ 
10mm
π‘‡π‘’π‘šπ‘π‘Ÿπ‘’π‘‘π‘’π‘Ÿπ‘’
β‰ˆ 1500k
Current
5A
πΈπ‘›π‘’π‘Ÿπ‘”π‘¦
140keV
2. DB Injector Thermionic Gun
11
2.2. Thermionic Gun Simulations (Beam Envelope)
πΆπ‘Žπ‘‘β„Žπ‘œπ‘‘π‘’
π‘π‘œπ‘ π‘’ π‘π‘’π‘›π‘‘π‘’π‘Ÿ
𝑅𝑅𝑀𝑆 = 3.6π‘šπ‘š
2. DB Injector Thermionic Gun
12
2.2. Thermionic Gun Simulations (Normalized Emittance)
πΆπ‘Žπ‘‘β„Žπ‘œπ‘‘π‘’
π‘π‘œπ‘ π‘’ π‘π‘’π‘›π‘‘π‘’π‘Ÿ
2. DB Injector Thermionic Gun
13
2.2. Thermionic Gun Simulations (Solenoid Channel)
𝐡 = 774 𝐺
πœ€π‘› = 5.8 π‘šπ‘š βˆ™ π‘šπ‘Ÿπ‘Žπ‘‘
2. DB Injector RF Gun
14
2.1. RF Gun Design (Specifications)
π‘·π’‚π’“π’‚π’Žπ’†π’•π’†π’“
𝑽𝒂𝒍𝒖𝒆
π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ 𝐢𝑒𝑙𝑙
1.6
πΉπ‘Ÿπ‘’π‘žπ‘’π‘’π‘›π‘π‘¦ 𝐺𝐻𝑧
1,2,3
𝑅𝑀𝑆 π΅π‘’π‘›π‘β„Ž πΏπ‘’π‘›π‘”π‘‘β„Ž 𝑃𝑆
10
πΆβ„Žπ‘Žπ‘Ÿπ‘”π‘’ π‘π‘’π‘Ÿ π΅π‘’π‘›π‘β„Ž 𝑛𝐢
8.4
π΅π‘’π‘›π‘β„Ž πΉπ‘Ÿπ‘’π‘žπ‘’π‘’π‘›π‘π‘¦ [𝐺𝐻𝑧]
0.5
πΆπ‘’π‘Ÿπ‘Ÿπ‘’π‘›π‘‘ [𝐴]
4.2
π‘ƒπ‘Žπ‘™π‘ π‘’ π‘…π‘’π‘π‘’π‘‘π‘Žπ‘‘π‘–π‘œπ‘› π‘…π‘Žπ‘‘π‘’ [𝐻𝑧]
50
𝐼𝑛𝑝𝑒𝑑 π‘ƒπ‘œπ‘€π‘’π‘Ÿ [π‘€π‘Š]
𝑒𝑝 π‘‘π‘œ 40
π‘ƒπ‘Žπ‘™π‘ π‘’ πΏπ‘’π‘›π‘”π‘‘β„Ž [πœ‡π‘†]
140
2. DB Injector RF Gun
15
2.1. RF Gun Designing (Designing &Optimization Algorithm)
Selection of a
Working Phase
for the cavity
Optimum
Structure
Matching the
beam to the
solenoid
channel and
simulate the
beam in acc
structures
Beam Loading calculations and find
the optimum coupling factor and
detuning with the goal of having
minimum input power
Designing the cavity with
this coupling factor and
calculate its electromagnetic
fields with CST
Beam dynamics simulations in
cavity fields with Parmela and
calculate the beam parameters
at the end of cavity
Change the
working
phase of the
cavity
2. DB Injector RF Gun
2.1. RF Gun Design (Beam Loading Optimization)
16
2. DB Injector RF Gun
2.1. RF Gun Design (RF Phase Optimization)
17
2. DB Injector RF Gun
18
2.1. RF Gun Design (Specifications of Optimum Structure)
π‘·π’‚π’“π’‚π’Žπ’†π’•π’†π’“
𝑽𝒂𝒍𝒖𝒆
π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ 𝐢𝑒𝑙𝑙
1.6
πœ‹ π‘šπ‘œπ‘‘π‘’ πΉπ‘Ÿπ‘’π‘žπ‘’π‘’π‘›π‘π‘¦ 𝐺𝐻𝑧
2
πΉπ‘Ÿπ‘’π‘žπ‘’π‘’π‘›π‘π‘¦ π·π‘–π‘“π‘“π‘’π‘Ÿπ‘’π‘›π‘π‘’ 𝑀𝐻𝑧
46
πΆπ‘œπ‘’π‘π‘™π‘–π‘›π‘” πΉπ‘Žπ‘π‘‘π‘œπ‘Ÿ
3.08
π‘„π‘’π‘Žπ‘™π‘–π‘‘π‘¦ πΉπ‘Žπ‘π‘‘π‘œπ‘Ÿ
17263
π΅π‘Žπ‘›π‘‘ π‘Šπ‘–π‘‘π‘‘β„Ž π‘˜π»π‘§
237
𝐹𝑖𝑙𝑙𝑖𝑛𝑔 π‘‡π‘–π‘šπ‘’ πœ‡π‘†
0.672
π‘†β„Žπ‘’π‘›π‘‘ πΌπ‘šπ‘π‘’π‘‘π‘Žπ‘›π‘π‘’ 𝑀Ω
3.165
π‘€π‘Žπ‘₯ πΈπ‘™π‘’π‘π‘‘π‘Ÿπ‘–π‘ 𝐹𝑖𝑒𝑙𝑑 𝑀𝑉/π‘š
99.83
𝑅𝐹 π‘ƒβ„Žπ‘Žπ‘ π‘’ 𝑑𝑒𝑔
35
𝑅𝐹 π‘ƒπ‘œπ‘€π‘’π‘Ÿ π‘€π‘Š
π‘ˆπ‘ π‘‘π‘œ 40
2. DB Injector RF Gun
19
2.1. RF Gun Design (Cavity Fields)
π‘·π’‚π’“π’‚π’Žπ’†π’•π’†π’“
𝑽𝒂𝒍𝒖𝒆
π‘˜π‘₯ 1/π‘š
29.3
π‘˜π‘¦ 1/π‘š
27.3
2. DB Injector RF Gun
20
2.1. RF Gun Design (Focusing Channel)
12 Accelerating Structures
Envelope Equation
π‘·π’‚π’“π’‚π’Žπ’†π’•π’†π’“
𝑽𝒂𝒍𝒖𝒆
𝐢𝑒𝑙𝑙 π‘π‘’π‘Ÿ 𝐴𝑐𝑐
24
𝐴𝑐𝑐 πΏπ‘’π‘›π‘”π‘‘β„Ž [π‘š]
2.4
𝐴𝑐𝑐 π‘‰π‘œπ‘™π‘‘π‘Žπ‘”π‘’ 𝑀𝑉
3.8
2. DB Injector RF Gun
21
2.2. RF Gun Simulations (Emittance & Envelope)
πœ–π‘› = 5.26
π‘₯π‘Ÿπ‘šπ‘  = 1.02
2. DB Injector RF Gun
22
2.3. RF Gun Simulations (Longitudinal Parameters )
RF
DC
2. DB Injector RF Gun
23
2.3. Comparison
π’„π’‰π’‚π’“π’‚π’„π’•π’†π’“π’Šπ’”π’•π’Šπ’„
𝑫π‘ͺ
𝑹𝑭
π‘π‘œπ‘Ÿπ‘šπ‘Žπ‘™π‘–π‘§π‘’π‘‘ πΈπ‘šπ‘–π‘‘π‘‘π‘Žπ‘›π‘π‘’ π‘šπ‘š βˆ™ π‘šπ‘Ÿπ‘Žπ‘‘
35
5
πΈπ‘›π‘’π‘Ÿπ‘”π‘¦ π‘†π‘π‘Ÿπ‘’π‘Žπ‘‘
1%
0.75%
Sπ‘Žπ‘‘π‘’π‘™π‘™π‘–π‘‘π‘’ π‘π‘œπ‘π‘’π‘™π‘Žπ‘‘π‘–π‘œπ‘›
2.1%
0
π΅π‘’π‘›π‘β„Žπ‘–π‘›π‘” π‘†π‘¦π‘ π‘‘π‘’π‘š
π‘Œπ‘’π‘ 
π‘π‘œ
πΏπ‘œπ‘›π‘”π‘–π‘‘π‘’π‘‘π‘–π‘›π‘Žπ‘™ π·π‘–π‘ π‘‘π‘Ÿπ‘–π‘π‘’π‘‘π‘–π‘œπ‘›
π‘‰π‘’π‘Ÿπ‘¦ π‘ˆπ‘›π‘–π‘“π‘œπ‘Ÿπ‘š
πΏπ‘œπ‘›π‘”π‘–π‘‘π‘’π‘‘π‘–π‘›π‘Žπ‘™ π‘ƒβ„Žπ‘Žπ‘ π‘’ π‘†π‘π‘Žπ‘π‘’
Vπ‘’π‘Ÿπ‘¦ πΆπ‘™π‘’π‘Žπ‘› & π‘†π‘¦π‘šπ‘šπ‘’π‘‘π‘Ÿπ‘–π‘
Work in Progress
Thanks for Attention

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