Transcript Constant Gradient Structure

Linear Accelerator (LINAC)
Juwen Wang 王聚文
SLAC National Accelerator Laboratory
July 30, 2014
全球华人物理和天文学会
第九届加速器学校
Xiuning, Anhui
Outline
1. Introduction: Brief History and RF Accelerator System.
2. Basic Ideas: Modes, Dispersion Curves and Structures Types.
3. RF Parameters for Accelerating Mode: Shunt Impedance,
Q, Filling Time, Phase & Group Velocity, Transient Time Factor, Attenuation
Factor, Coupling Coefficient.
4. Basic Beam Dynamics: Acceleration, Bunching and Beam
Loading.
5. Wakefield: Longitudinal and Transverse Wakefield.
6. How to Make a Linac: Machining, Chemical Cleaning, Diffusion
Bonding & Brazing, Tuning & Microwave Measurement, Vacuum Baking,
Fiducialization, High Power Processing.
* .Some topics are mainly for room temperature RF structures.
2
1. Introduction
• High Voltage Linac and RF Linac.
• Brief History of RF Linac.
• Building Blocks of RF Linac
3
High Voltage Accelerator and
Radio Frequency RF Accelerator
Van de Graff Accelerator
RF Accelerator
4
Brief History of RF Linac
The first formal proposal and experimental test for a RF linac was by Rolf Wideröe
in 1928. The linear accelerator for scientific application did not appear until after
the development of microwave technology in World War II, stimulated by Radar
program.
1955 Luis Alvarez at UC
Berkeley, Drift-Tube Linac (DTL).
1947 W. Hansen at
Stanford, Disk-loaded
waveguide linac.
1970 Radio
Frequency Quadruple
(RFQ)
5
Building Blocks of RF Linac
RF
Control
System
Vacuum
System
Water
Cooling
System
RF Power
System
6
2. Basic Ideas
•
Electromagnetic Wave and Waveguide
•
Wave Propagation Equations
•
Waveguide Modes
•
Dispersion Properties
•
Periodic Structure and its Dispersion Properties
7
Basic Data and Formulae
E total Energy
E0 rest energy
W kinetic energy
m mass, m0 rest mass
γ relative mass factor
c speed of light
v velocity
β normalized velocity
Speed of light
c 2.998x108 m/s
Elementary charge
e 1.6x10-19 C
Electron mass
me 0.51 MeV/c2
Proton mass
mp 938.3 MeV/c2
p momentum
FLorentz Lorentz force
q electrical charge
𝐸 electric field
𝐵 magnetic field
8
Electron and Proton
Velocities vs. Kinetic Energies
9
Wave Propagation Equations
Wave equation for propagation characteristics:

2
 Ek E 0
2
k   / c  2 / 
ω is the angular frequency 2πf and k is wave number (radian per unit length) of plane wave
in free space.
In a cylindrically symmetric waveguide, the transverse magnetic field does not have φ
dependence for most simple accelerating modes. All field components can be derived from
Ez in cylindrical coordinates and it satisfies the wave equation:
 2 Ez
r 2
2

1 E z   
2

      E z  0
r r
 c 

β=2π/g is propagation constant and g is called guide wavelength.
For perfect metal boundary condition at waveguide wall, Ez = 0, this boundary condition
decides the ωc, which is called cut-off frequency.
 
 
2
2
      c   kc
c
 c 
We will use that ω and β to characterize the wave properties – Dispersion Property
2
2
10
Solution of Wave equation
The solution for TM01 mode (lowest mode) is as followings:
E z  E0 J 0 kc r e j (t  z )
Er  jE0
1  (c /  ) 2 J1 (kc r )e j (t  z )
H  jE0 J1 ( kc r )e j (t  z )
On the axis:
J 0 (0)  1  E z (0)  Max.
On the wall:
J 0 (kc b)  0  E z (b)  0
The first zero of J0:
Hf
EZ
r
kc b  2.405
c  kc c  2.405c / b
For example, in a cylinder with wall diameter 2r = 2b= 9 cm, fc = 2.55 GHz,
A electromagnetic wave with f =2.856 GHz (S-Band)
𝜷 = 𝟐𝝅
𝒇
𝒄
𝟐
𝒇𝒄
−
𝒄
𝟐
>𝟎
Therefore, this wave can propagate as TM01 mode in this cylindrical waveguide.
11
Simple TM01 Mode
50
0
0
0.2
J 0 kc r 
J1 kc r 
0.5
1
/c r
1.5
2
0.1
Bf (T)
For a case of ω ~ 1.2ωc
EZ (MV/m)
100
0
2.5
12
Dispersion Curve
for TM01 Mode in a Cylinder
The phase velocity Vp is the speed of RF
field phase along the accelerator, it is
given by
Vp 


Vp>c
Group velocity is defined as energy propagation
velocity.
For wave composed of two components with
different frequency ω1 and ω2 wave number β1 and
β2 , the wave packet travels with the velocity:
Vg 
1   2
d

1   2
d
Hyperbola ω-β diagram for guided wave in a
uniform (unloaded) waveguide.
For uniform waveguide, it is easy to find:
Vp  c
vp=c
VpVg  c2
 
2
kc      2
c
2
In order to use RF wave to accelerate particle beam, it is necessary to
make simple cylinder “loaded”. The variety of accelerator structures have
been created.
13
Dispersion Curves
for Periodic Structures
Brillouin (ω-β) diagram showing propagation characteristics for
uniform and periodically loaded structures with load period d.
Floquet Theorem: When a structure of infinite length is displaced along its axis by one period
2π/d, it can not be distinguished from original self. For a mode with eigen frequency ω:
 
 jd
 



E( r , z  d )  e
E( r , z) r  x x  y y where βd is called phase advance per period.

Make Fourier expansion for most common
E z   an J 0 (k rn r )e j (t   nt )
accelerating TM01 mode:

Each term is called space harmonics.
2
2n  2n
2
2
k

k








n
0
14
rn
n
The propagation constant is
d
VPo
d
Discussion on Some Facts
for Better Understanding
• It is interesting to notice that for the fundamental harmonic n = 0 travels
with Vp = c, then kr0 = 0 , β0 = k and J0(kr0 r)=1, the acceleration is
independent of the radial position for all synchronized particles.
• Each mode with specific eigenfrequency has unique group velocity for all
space harmonics. The total field pattern or distribution is decided by the
coefficients of those components – decided by the cell profiles like iris size,
disk thickness. (later, we will see how these space harmonics add
together).
•We need design the structure have higher effective fundamental
harmonics (later, we will talk about high transient factor structures)
• Every higher order space harmonics does not have contribution to
acceleration, but takes RF power. (later, we will know that they contribute
to wakefield).
15
Electrical Field Patterns
for Periodic Structures with Different Modes
Mode is defined as the “phase shift” or “phase advance”
per structure period:
Phase shift / cavity = 2π/(cavity number per wavelength)
16
SW & TW Structures
pulsed RF
Power
source
d
pulsed RF
Power
source
Constant Impedance Structure (CI)
Standing Wave Structure
d
Traveling Wave Structure
RF
load
Constant Gradient Structure (CG)
17
Evolution from Single to Bi-period
Structures
π
π
π
18
3. RF Parameters for Accelerating Mode
• Shunt impedance,
• Q,
• Filling time,
• Phase & Group velocity,
• Transient Time Factor,
• Attenuation factor,
• Coupling coefficient.
19
Particle Acceleration in a Cavity
Time various accelerating field
Acceleration integrated in a cavity
Ez  Ez (r, z, t )  Ez (r, z) cos(t  f )
L/2
W  q
L/2
 E dz  q  E ((0, z) cos(t ( z)  f )dz
z
L / 2
z
L / 2
Choose the field is maximum while particle in the center of cavity (z=0)
 L/2

E
(
0
,
z
)
cos(

t
)
dz


 L / 2
   L/ 2 z
  qV T
W  q   E z (0, z )dz
0
L / 2


 L / 2

E z (0, z )dz



L / 2


L/2
T is defined is as
the Transient Time Factor
 E (0, z) cos(t )dz
z
T  L / 2 L / 2
 Ez (0, z)dz
L / 2
-- True integration of
acceleration
-- Integration of amplitude
of acceleration field
20
Main RF Parameters –
Shunt Impedance
Shunt impedance per unit length r and R for structure length L
which measure the accelerating quality of a structure and is defined as
2
Ea
r
Unit of MΩ/m or Ω/m
dP / dz
where Ea is the synchronous accelerating field amplitude and dP/dz is the
RF power dissipated on the accelerator walls per unit length;
for a certain structure
with length of L,
the shunt impedance is
2
Ea L2
V2
R

(dP / dz) L Pd
Ez (r, z) r 0  Ez (0, z)
2
Unit of MΩ or Ω
(some code called z0)
2
 L / 2

 L / 2

E
(
0
,
z
)
cos(

t
)
dz
E
(
0
,
z
)
dz
  z

  z

2
Ea
  T 2   L / 2
  zT 2
r
   L / 2
2
2
dP / dz
dP / dz  L
dP / dz  L
L/2
 E (0, z)Costdz
z
T
where T is defined as
L / 2
L / 2
 E (0, z)dz
z
L / 2
often it is calculated and listed in
some codes.
21
Main RF Parameters – Factor
of Merit and Group Velocity
Factor of merit Q, which measures the quality of an RF structure as a
resonator.
• For standing wave structure W is the
RF energy stored in a cavity.
Q
W
Pd
 w
• For traveling wave structure, w is the
Q
dP / dz
RF energy stored per unit length and
dP/dz is power dissipated per unit
length.
Group velocity Vg, which is the speed of RF energy flow along a TW
accelerator:
Power flow = Group velocity
times Stored energy per unit
length:
P  Vg w
Vg 
P
 P
d


w QdP / dz
d
22
Main RF Parameters –
Attenuation Factor
Attenuation factor ԏ, which is the measure of power reduction due to RF
Ohm loss along a Traveling Wave accelerator.
dE
  ( z ) E
dz
P out
 e  2
Pin
α(z) is the attenuation coefficient
in nepers per unit length.
dP
 2 ( z ) P
dz
ԏ is the attenuation factor in nepers of the
total structure.
• For a constant-impedance section with a length L, the attenuation is uniform:

 dP / dz w / Q



 const
2P
2Vg w 2Vg Q
  L 
L
2Vg Q
• For a constant-gradient section (E=const):
the attenuation constant α is a function of z:
Pin (1  e 2 )
dP / dz  2 ( z ) P  const 
L
• For any non-uniform structures:
(
   ( z) 
dP
 2P  const )
dz

It is not a constant
2Vg ( z )Q as a function.
L
    ( z )dz
0
23
Main RF Parameters –
Filling Time
Filling time tF
• For traveling wave structure, the field builds up “in Space”. The filling time is the time
needed to fill the whole section of either constant impedance or constant gradient, which is
given by
L
L
L
dz Q  dp / dz
Q
2Q
 
dz   2 ( z )dz 

V

P


g
0
0
0
tF  
Before to talk about the filling time for standing wave cavity, let briefly discuss about coupling
parameters for standing wave cavity in a coupling system including cavity and external circuit.
System Q or Loaded QL=(stored Energy)/Dissipated energy in both cavity and external circuit):
Coupling coefficient β of
the cavity to the input
microwave network is
Q
 0
Qe
P
P
1
1
1
 0  e 

QL W0 W0 Q0 Qe
Q0 is the unloaded Q value,
Qe is external Q value,
QL is loaded Q value,
QL 
W0
P0  Pe
Q0 = ωW0 /P0 ,
Qe = ωW0 /Pe = Q0/β ,
QL = ωW0 /(P0+Pe)=Q0/(1+β) .
• The field in SW structures builds up “in Time”. The filling time is defined as the
time needed to build up the field to (1  1 ) = 0.632 times the steady-state field:
e
tF 
2QL


2Q0
(1   )
24
Main RF Parameters –
r/Q Ration and Frequency
r/Q Ratio is a important factor, which is only depending on geometry
of the structure to evaluate its accelerating ability.
r
E2
dP / dz E 2



Q dP / dZ
w
w
E2/w is independent with material, machining quality of the structure.
Working Frequency is a first and important parameter to choose in
accelerator design.
Almost all basic RF parameters have frequency dependence, they are
scaled as the following:
1
size 
f
r
f
Q  1/
f
r
 f
Q
25
4. Basic Beam Dynamics
• Acceleration
• Bunching
• Beam Loading
26
Acceleration for Constant Impedance
TW structures
• For a constant-impedance section with a length L, the attenuation is uniform:
From the α
definition:
dP
 2（z ) P  2 0 P
dz
P( z)  P0e20 z
Integration
result:
E 2  r (
dP
 z
)  2 0 rP E  2 0 rP0 e 0
dz
dE
  0 E
dz
z
V ( z )   E ( z )dz  2
0
(1  e
0 z

)
P0 rL






Per unit length 0 2V Q  const
g
  0 L 
Total length
L
2Vg Q
E( z)  E0e0 z
P( z)  P0e20 z
E(0)  E0
V (0)  0
E( L)  E0e2
(1  e )
V ( L)  2
P0 rL

27
Acceleration for Constant Gradient
TW structures
• For a constant-gradient section (E=const):
the attenuation constant α is a function of z:
P0 (1  e 2 )
dP / dz  2 ( z ) P  const 
L
 z

P( z )  P0 1  1  e 2  Liner reduction along the structure
 L

1  e 
Combine above  ( z )  1
2L  z
two equations:
 2 


1

1

e

2


z
1  1  e  2 

L
L
Vg ( z ) 

1  e 2 
2Q ( z ) Q
E 0  r
2
L
dP rP0

(1  e  2 )
dz
L
V  E0 L  1  e 2
P0 rL
28
Summary of Acceleration in TW structures
1.
The energy gain V of a charged particle is given by
CI:
V  2
(1  e
 0 z

)
P0 rL
CG:
V  1  e 2
P0 rL
2. The RF energy supplied in the time period tF can be derived from above:
CI:
 
2
2
 V
P0t F  
 
1

e

 r L
Q
CG:
 2
P0t F  
 2
1 e
2
 V

 r L
Q
3. The energy W stored in the entire section at the end of the filling time is
l
CI: W  Q dp dz  P0 Q (1  e 2 ) CG:
 0 dz

l
P
Q
W   dz  P0 (1  e 2 )
v

0 g
29
Acceleration for SW structures
P  Ps  Ps e
 2L
 Ps e
 4L
Ps
 ..... 
1  e  4L
The slightly higher energy gain for SW is paid by field building
up time. The energy gain of a charged particle is given:
V  (1  e
t / tF
)
2 c
1  c
Pin rL  (1  e t / t ) PdisrL
F
Where βc is coupling coefficient between waveguide and structure.
30
An Example – Field Plot
by SUPERFISH Code
Location of
Maximum Field
Meshes and electrical field lines in one and half cell
for a SLAC 2π/3 mode, 2856 MHz structure.
31
An Example – Calculation of RF
Parameters by SUPERFISH Code
Note: Often, the computer calculation codes give parameters for SW case – field is a snapshot of TW case at certain
moment to meet boundary conditions. Therefore, interpretation for TW is different. For example, shunt impedance
needs to have factor of 2, because the backward wave does not have contribution to acceleration.
32
Longitudinal Dynamics
Speed of particle: 𝛽𝑒 = 𝑉𝑒 /𝑐  e   2  1 /  Phase speed of acceleration RF: 𝛽𝑝 = 𝑉𝑝 /𝑐
m Ve
Normalized momentum of particle: p 
 e   2  1 and  2  p 2  1
Energy of particle:
   (
u
m0 c
2
1   e2
m0 c
 m0 c 2
1 1
2  c 1 1
1 1
 )dz 
(

)
dz

k
(
  p  e )dz
Vp Ve
  Vp Ve
The longitudinal motion is described by the following two equations:

du
  eE z Sin
dz
The reference phase is θ=0 without acceleration
d 2  1
 


dz    p
 2  1 
Combining above two formula:
2  1
 

du  eEo sin d
2

   p
 1 
We have the solution:

kmo c 2  p 2  1
cos 
 p   const

eE0   p


33
Longitudinal Phase Space for βp<1
Stable particles stay within the structure circulating
Phase velocity less than c (βp<1)
 2 1
with phase extreme    m while
e 
 p

const  cos m 
2m0c 2
cos  cos m 
eE0 p

km0c
eE0
2
1  p
2
p
p 2  1  1   p2   p p
When 1>cosθ>-1 the particles oscillate in
p and θ plan with elliptical orbits. If an
assembly of particles with a relative large
phase extent and small momentum extent
enters such a structure, then after
traversing ¼ of a phase oscillation it will
have a small phase extent and large
momentum extent, we call this action as
bunching.

34
Longitudinal Phase Space for βp=1
Phase velocity equals c (βp=1)
When βp=1, dθ/dz(βe<1) is always
negative, and the orbits become openended as shown in the figure. The orbit
equation becomes
2m0 c 2
cos  cos m 
eE0 


2m0 c 2
p 1  p 
eE0 
2
1  e
1  e
where θm has been renamed θ∞ to
emphasize that it corresponds to p  ∞ .
35
Longitudinal Dynamics - continued
The threshold accelerating gradient for capture is cosθ-cosθ∞= 2, or
For example, the field of 15.3MV/m
m0c 2 

at 2856 MHz can capture dark
E (threshold ) 
p 2 1  p 

0
0
e  0
current (starting with p0~0).
Let us discuss an interesting case: a particle entering the structure with a phase θ0=0,
has an asymptotic phase θ∞= -π/2, thus the an assembly of particles will get maximum
acceleration and maximum phase compression. For small phase extents ±Δθ0 around
θ0=0,
( 0 ) 2
  
8
Let us consider a practical example at SLAC (λ=10.5 cm). Over a wide range of
electrons enter an accelerator section with optimized accelerating gradient and
have the above idea bunching to better than 5O bunch.
Asymptotic bunching process in Vp=c
constant-gradient accelerator section
with value of accelerating gradient E
optimized for entrance condition.
36
Beam Loading - I
The effect of the beam on the accelerating field is called BEAM LOADING.
The superposition of the accelerating field established by external
generator and the beam-induced field needs to be studied carefully in order
to obtain the net Phase and Amplitude of acceleration.
Steady-state Phasors in a complex
plane for beam loaded structure:
Vg generator-induced voltage
Vb beam-induced voltage
Vc net cavity voltage
In order to obtain a basic physics picture, we will assume the
synchronized bunches in a bunch train stay in the peak of
RF field for both TW and SW analysis.
37
Beam Loading - II
The RF power loss per unit length is given by:
dP
dP
dP
 ( ) wall  ( )beam
dz
dz
dz
E 2  2rP
dP
 2P
dz
E2
r
dP / dz
dE
d
dP
E 2 d
 E2

E
 rP
 r
r
 r 
 EI 
dz
dz
dz
2r dz
 r

where I is average peak current, E is the amplitude of synchronized field.
dE
1 d 

 E 1 
  rI
2
dz
dz 
2

38
Beam Loading
for Constant Impedance Structure
For constant impedance structure:
dE
  0 E   0 rI
dz
E( z)  E(0)e0 z  Ir(1  e0 z )
E (0) 
2 0 rP0
The total energy gain through a length L is
L
V   E ( z )dz 
0
2
(1  e
 0 z

)
P0 rL  IrL (1 
1  e 

)
where P0 is input RF power in MW, r is shunt impedance per unit length in
MΩ/m, L is structure length in m, I is average beam current in Ampere, V is
total energy gain in MV.
The first term is unloaded energy gain, and loaded energy decreases
linearly with the beam current.
39
Beam Loading
for Constant Gradient Structure
For constant gradient structures:
The attenuation coefficient is
After integration:
 ( z) 
E  E0 
dE
 rI
dz
(1  e 2 ) / 2 L
1  (1  e  2 )( z / L)
rI
z


ln1 
(1  e  2 ) 
2
L


The complete solution including transient can be expressed as:
tF  t  2tF


 2
 t 
rI  Le
L
Q 
V (t )  E 0 L 
t

(
1

e
)
 2

2  Q (1  e 2 )
1 e



2e 2 
1 
2 
1

e


Steady case after two filling time.
t  2t F
rIL
V (t )  E0 L 
2
Transient beam loading
in a TW CG structure.
40
Beam Loading
for Standing Wave Structure
For a standing wave structure with a Coupling coefficient βc,
The energy gain V(t) is
t / t F 2  c
V (t )  (1  e )
PinrL  (1  et / tF ) Pdis rL
Without beam loading
1  c
t t
 b
irL
t / t
(1  e tF )
With beam loading V (t )  (1  e F ) Pdis rL 
1 
If the beam is injected at time tb and the coupling coefficient meets the following conditio
Pb
c  1
Pdis
We will have:Pin
 Pdis  Pb
There is no reflection from the structure to
power source with beam. From above
formula, the beam injection time is
Vb
2 c
t b  t F ln(1  )  t F ln
V0
 c 1
Transient beam loading in a
standing wave structure.
41
Example of Beam Loading
Compensation for TW Structure
Beam injection is started before filling complete structure
42
5. Wakefields
•
•
•
•
What is Wakefield
Longitudinal Wakefield
Transverse Wakefield
Examples of Wakefield
Mitigation and Measurement
43
Wakefields
The wakefield is the scattered electromagnetic radiation created by
relativistic moving charged particles in RF cavities, vacuum bellows,
and other beam line components. These fields effect on the particles
themselves and subsequent charged particles.
Electric field lines of a
bunch traversing through
a three-cell disc-loaded
structure.
 No disturbance ahead of moving charge ----- CAUSALTY.
 Wakefields behind the moving charge vary in a complex way – in space and time.
 The fields can be decomposed into MODES.
44
Longitudinal Wakefields - I
We define the longitudinal delta-function potential
Wz(s) as the potential (in Volt/Coulomb) experienced
by the test particle following along the same path
with distance s behind the unit driving charge.
1
zs
Wz ( s )    E z ( z ,
)dz
Q0
c
L
 Each mode of wakefiekds has its particular FIELD
PATTERN and oscillates with its own eigenfrequency.
 For simplified analysis, the modes are orthogonal, i.e.
the energy contained in a particular mode does not has
energy exchange with other modes.
Notations for a point
charge traversing
through a discontinuity.
45
Longitudinal Wakefields - II
The longitudinal wakefields are dominated by the m=0 modes, TM01, TM02,….
0( s  0)
s
Wz ( s)   kn cos( n )  1( s  0)
c
n
2( s  0)
kn 
Vn
2

n Rn
(
)
4U n
4 Qn
The loss factor kn:
where Un is the stored energy for nth mode.
Vn is the maximum voltage gain from nth mode for a unit test particle with
speed of light.
The total amount of energy deposited in all the modes
by the driving charge:
U  Q 2  kn
n
• Longitudinal wakefields are approximately independent of the transverse positions of
both the driving and testing charges.
• Impact of Short range longitudinal wakefields --- Energy spread within a bunch.
• Impact of Long range longitudinal wakefield --- Beam loading effect.
46
Longitudinal Wakefields - III
Computed longitudinal δ- function
wake
potential per cell for S-Band SLAC
structure:
Solid line: Total wake
Dashed line: 450 modes
Dot-dashed line: Accelerating mode
47
Transverse wakefields - I
The transverse wake potential is defined as the
transverse momentum kick experienced by a unit test
charge following at a distance s behind on the same
path with a speed of light.
L
1
   
W   dz E  ( v  B)  
Q0 
t  zs
c
The transverse wakefields are dominated by the dipole
modes (m=1), For example, HEM11, HEM21,…
Approximately:
2k1n
1n s
r' 
W  ( ) x 
Sin(
) s0
a
c
n 1n a / c
E
Field
B
Field
In phase
quadrature
Schematic of field Pattern
for the lowest frequency
mode -- HEM11 Mode.
where r´ is the transverse offset of driving charge and the charge is on x axis.
a is the tube radius of the structure.
k1n for m=1 nth dipole mode has similar definition like m=0 case.
The unit of transverse potential V/Coulomb/mm.
The transverse wakefields depend on the driving charge as the first power of
its offset r’, the direction of the transverse wake potential vector is decided by
the position.
48
Transverse wakefields - II
Single Bunch Emittance Growth (HeadTail Instability) due to the short range
transverse wakefields
Computed transverse δ-function wake potential
per cell for S-Band SLAC structure.
Solid line: Total wake
Dashed line: 495 modes
Dot-dashed line: lowest frequency dipole
mode (λ=7 cm)
Multi-bunch Beam Breakup
due to the long range
transverse wakefields.
49
Long Range Dipole Mode Suppression
- Idea of Detuning of Dipole Modes
Cells for a Detuned Structure have profiles with Gaussian dimensional distribution.
k
dn
df1
In frequency domain, dipole
mode distribution for a Detuned
Structure
In the time domain, the excited wakefields by
the cells with Gaussian distribution dipole
frequencies has Gaussian amplitude profile.
50
Experimental Proof of Transverse
Wakefield Suppression
10
Calculation
ASSET Data
Wake (V/pC/mm/m)
Comparison of the measurement
with error bars (red) and
calculated wakefields (black) for a
pair of dipole modes Interleaved
60 cm Damped Detuned X-Band
Structures.
2
10
10
10
10
1
0
-1
-2
0
5
10
15
20
Time (ns)
25
30
35 51
6. How to Make a Linac
•
•
•
•
•
•
•
Machining
Chemical Cleaning or Electrical Polishing.
Diffusion Bonding and Brazing
Tuning and Microwave Characterization
Vacuum Baking
Fiducialization and Assembly
High Power Processing and Testing
52
Computer Numeric Control (CNC) lathe
and Some Machined Linac Parts
53
Chemical Cleaning – Critical Step
for All High Power RF and High Vacuum Parts
• Decreasing
• Chemical Etching (Contaminations,
Mechanical Defects,
Surface Roughness …)
• Anti-Oxidation Treatment
54
Diffusion Bonding of Linac Body
Pressure: 60 PSI (60 LB for this structure disks)
Holding for 1 hour at 1020º C
55
Brazing Linac in a Hydrogen Furnace
56
Non-Resonant Perturbation Measurement
Reflected wave amplitude is
E 2 ( z)
Er ( z )  K
Ei ( z )
P( z )
where K is a constant, which depends on the bead, E(z) is the forward
power flowing across the structure at z, Ei is the incident wave amplitude.
The reflection coefficient is defined as:
E ( z)
 ( z)  r
Ei ( z )
For constant gradient structure:
Er (0)
E 2 ( z)
 (0) 
K
 S11
Ei (0)
P(0)
57
Tuning and
Structure Characterization
• Set the bead pulling
frequency with correction for
string perturbation, operation
temperature correction, dry
nitrogen environment.
• Record amplitude and phase
of S parameters while bead
puling through the structure.
• Program to calculate the
detuning amount of cell n th
based on the backward
reflection difference from (n-1)
th disc and (n+1) th disc.
• Tuning each cell to the target
value.
58
Microwave Tuning and Characterization
for a CLIC Prototype Structure
59
Example of Phases and Amplitudes
along the Axis of CLIC Prototype Structure
Phases and amplitudes plotted
in a complex plane (2π/3 mode
structure, 2x120º=240º per cell
for reflection)
Electrical field amplitudes along the structure.
60
Final Parameters Measurement
Very Small Reflection from Input and Output Ends and Required Transmission
Input End S11
Transmission S12
Output End S22
61
Some Very Useful Relations
for Any TW Structures Analysis
L
L
dz
Tf  
V
0 g
f    dz
0
If the operation temperature (or resonant frequency for every cell)
changes with Δω.
f
d
dz
  dz    T f
 0 d
V
0 g
L
L
The total phase drift due to frequency change is:
f  2  f  T f
Example: If particles with speed c passing a Vp =c and T=100 ns structure.
Case I: Operation frequency Δ f=1 MHz, phase slippage ΔΦ=36°
Case II: Temperature change to cause heat expansion and frequency change.
f
 1.66105 / C O
f
Let’s assume the structure frequency is 11424 MHz, the resonant frequency
change is 1.66105 11424103  0.19MHz / C O
Use above formula, the total phase slippage is 7O per Cº .
Vacuum Baking of Two Linac Structures
650° C
for10 days
63
Fiducialization and Alignment
In a CMM machine for an X-Band Deflector
64
Complete Instrumentation for
RF High Gradient Experiments
Outgassing
RGA
Vacuum Gauge
X-Ray
PMTs
Scintillators
Ion Chamber
Dark Current
Profile Monitor
Spectrometers
Faraday Cup
RF Breakdown
Forward/Reflected
RF Instruments
Surface Damages
SEM, XPS, EDX
65
Wish You All
Great Success in your Career!
66