Transcript CERN_exp1

The thinner the ice, the more anxious is
everyone to see whether it will bear.
Billings
PROPOSED EXPERIMENTS AIMED AT RAISING THE RF
BREAKDOWN THRESHOLD IN A MULTI-MODE CAVITY#
S.V. Kuzikov1,2, S.Yu. Kazakov1,3, J.L. Hirshfield1,5, M.E. Plotkin2,
A.A. Vikharev2, V.P. Yakovlev1,4
1Omega-P,
Inc., New Haven, CT, USA
2Institute of Applied Physics, Nizhny Novgorod, Russia
3KEK, Tsukuba, Japan
4Fermi National Accelerator Laboratory, Batavia, IL, USA
5Yale University, New Haven, CT, USA
#
Work sponsored by in part by US Department of Energy, Office of High Energy Physics (2009).
OUTLINE OF TALK
1. The main idea is to attempt to raise RF breakdown thresholds by reducing the
exposure time of surfaces to high fields, by use of multi-mode cavity excitation.
2. General scheme of the experiments is to build test cavities to be driven by a highcurrent bunched beam, with cavity mode frequencies that are harmonic multiples.
3. Why should this experiment be interesting for CLIC?
4. Why do we need CTF-3?
5. Two cavity geometries can be used to test this idea:
1. Rectangular cross-section cavities; and/or
2. Axisymmetric cavities.
6. Results of preliminary calculations using CTF-3 parameters:
1. RF E-field analysis in 1-, 2-, and 3-mode cavities;
2. RF magnetic field analysis and pulse heating estimates; and
3. Preliminary analysis of multipactor threat.
7. A second related idea is to attempt to raise RF breakdown thresholds by using a
two-mode, two-frequency axisymmetric, but longitudinally asymmetric cavity.
8. Methodology and possible time-schedule for the proposed experiments.
9. Accelerating structures and other ideas.
10. Summary.
Principle of acceleration in a multi-frequency structure
E-field
A
vb
vb
E ||
beam line port
bunches
bunches
Acceleration of moving periodical sequence of
bunches in independent cavities,
operated by superposition of synchronized modes
A
1
2
3
t
E-field in A-A cross-section
1 – ideal (desired) time-dependence of the field,
2 – time-dependence of the field in an ordinary single-frequency structure,
3 – time-dependence of the field in a multi-frequency structure (with finite number of modes)
This solution is periodical in time, therefore, spectrum of the eigen modes of the
cavities has to be equidistant one!
l
lb
 
 
Tb  b
c
E (r , t )   a n  Fn (r )  exp( i n t ),
bunches (vc)
n
n  0  n  ,
where n=0,1,2,…
 
 
E (r , t )  exp( i0t ) an  Fn (r )  exp( i  n  t ),
 
  n
E(r , t  Tb )  E(r , t ),
Here 0/=p/q, where p and q are arbitrary integers.
E||
bunches
Tb
t cor
t
If taking finite number of modes, single peak duration is defined by the time, during which mutual
phase of the lowest-frequency and highest-frequency modes reaches :
tcor 

 N  0
Raise of breakdown threshold due to reduction of exposure time
A breakdown can be separated at several stages:
 At the primary stage RF electric field produces electrons to
tunnel from microjuts, this effect is described by the FowlerNordheim law.
 At the second stage the microjuts are melted and
evaporated.
The freed molecules are ionized by oscillating electrons.
The resulting plasma frequency grows up and approaches
the field frequency.
In [W. Wuensch et al, 2008] it is suggested to consider the first stage only, in order
to find criteria of the breakdown ignition. According to that necessary condition to
start a breakdown is a heating of surface by emission currents up to definite
threshold temperature Tthr.
The temperature rise T as a function of time t (with heat diffusion into metal taken
into account):
t
j (t )  E (t )
T (t )  A  
dt ,
t  t
0
j – is a tunnel emission current, E- is a normal to surface field component, A – is
a constant
E 3 (t )  exp(  / E (t ))
T (t )  B  
dt ,
t  t
0
t
where the expression behind integral is assumed to be different from zero if only E(t)>0,
B and  – are constants.
3
Ethr
 t 1 / 2  const
HG Workshop, W.Wuensh, 2008
or
6
Ethr
 t  const  I .
E(t) and I(t) dependencies for single(1) and multi-frequency (2) structures
Note that positive field maxima are essentially
bigger than absolute values of the negative
maxima.
additional
time-factor
2! on time for single 3 GHz cavity and
Field dependence
on time forThis
singlebrings
3 GHz cavity,
for 15
Field dependence
GHz cavity, and for 3+9+15 GHz multi-mode cavity.
for 3+6+9 GHz multi-mode cavity.
In this case we expect raise of breakdown
threshold due to reduction of exposure
time ~51/6=1.3.
In this case we expect similar raise of
breakdown threshold due to reduction of
exposure time ~(2*(9-3)/3)1/6=1.26.
However, there are not experimental proofs of breakdown theory validity in case
of a complicated microstructure of RF radiation.
If you don’t know where you’re going, you’ll end up somewhere else.
Yogi Berra
We suggest to build three cavities to be excited
identically (by means of the same e-beam).
We would like to compare probabilities of breakdown in
these three cases: 1-, 2-, and 3-mode cavities.
The cavities design should provide the same E-field
level, in order to deal with effect of the different
exposure time only.
 It is expected that 3-mode cavity will be most
breakdown proof among all others.
bunches
Lb
a
Lr
Why should such experiment be interesting for CLIC?
•
•
The experiment is aimed to investigate fundamental basis of the modern RF
breakdown theory:
We plan to investigate dependencies of the breakdown threshold on the shape of
RF microoscillations.
People already investigated dependencies on the field magnitude and
pulse duration as well. The only light spot is a dependence on shape of RF filling!
If a raise of the threshold will be shown, it opens a new way to accelerate particles
with a higher gradient than usually.
Why do we need CTF3?
Our simple answer is that we are asking to use a unique facility of the CTF3 for
fundamental tests in accelerator R&D.
To our knowledge, there is no other GHz-rate, high-current, high-quality beam in
another lab to which we have access.
The ANL drive beam consists of one bunch or, possibly in future, a maximum of 16
bunches. This is not enough to charge up our cavities.
There is a proposal of Sergey Kazakov to use two KEK’s klystrons, in order to feed a
two-frequency cavity. But this is absolutely another story…
List of CTF3 parameters used in calculations:
Electron energy, MeV
120
Bunch charge, nC
2.33
Bunch diameter, mm
23
Bunch length, mm
2
Bunch frequency, GHz
3
Train length, s
Repetition rate, Hz
assumed to be reduced to 15 mm
by means of quadrupole doublets
0.693
1
Two geometries of test cavities were considered:
Rectangular cross-section cavities
Circular cross-section cavities
Rectangular cross-section cavities
Such a cavity is the simplest example of a system having equidistant mode spectra.
3-mode cavity
mode
frequency, GHz
Q-factor
TM110
3.00
6220
TM330
9.02
11090
TM550
15.00
14480
mode
frequency, GHz
Q-factor
TM110
3.02
6110
TM330
8.98
10450
TM550
14.85
330
mode
frequency, GHz
Q-factor
TM110
3.00
5450
TM330
9.64
570
TM550
15.13
80
2-mode cavity
Single mode cavity
Unfortunately, properties of the cavity with beam hole are essentially
different from properties of the unperturbed cavity.
Three-mode axisymmetric cavity with modes at 3 GHz, 6 GHz, and 9 GHz
Beam channel
E-fields of eigen modes
waveguide
hole for
e-bunch
cavity
quartz window
arc detector
Design with side waveguides (cut off frequency is slightly more than 9 GHz) provides:
1. Autofiltration of spurious modes,
2. Visual control by means of arc detector and fast camera (through quartz windows).
Single mode cavity at 3 GHz
Beam channel
E-field of the operating mode
Magnetic field of the operating mode.
Maximum of E-field at surface is close to the correspondent maximum in 3-mode cavity.
Great intellects are skeptical.
Nietzsche
What results do we expect to obtain in the end?
1. Optimistic case
We prove that reduction of exposure time allows increasing breakdown threshold.
This proof gives a green light for all calculations based on the present breakdown
theory. A raise of threshold would allow to invent new structures with higher
gradient.
2. Pessimistic case
We do not see difference between cavities (taking into account the accuracy of the
experiment)
This requires to reconsider the breakdown theory!
3. The worst case
We can not state neither (1) nor (2).
Such result could be because influence of so-called not taken into account factors:
1. Pulse heating
2. Multipactoring
Pulse heating effect in the 3 GHz cavity
Magnetic field of the operating mode.
Temperature rise is about 70 degrees C.
Pulse heating effect in the 3-mode cavity
Magnetic fields of the 1st, 2nd, and 3rd modes.
Temperature rise in three-mode cavity is ~60 degrees C.
In two-mode cavity T~ 50 degrees C.
This temperature level allow working at least up to ~106 pulses [Tantawi et al, 2008].
Preliminary multipactor analysis



 2r
v 
m 2  eE  e   H - equation of electron motion by Lorentz force
t
c
Electron motion can be respresented as a sum of fast oscillations and slow drift:



r (t )  rfast (t )  Rslow (t )
The second term describes slow average motion (drift) of an electron in electric
and magnetic RF fields

2
2R
eE

- Miller force
 , where  
t 2
2m
Potentially dangerous places in viewpoint of multipactor are where electric field
magnitude and Miller force go to zero simultaneously. These places corresponds to
stable equilibriums (red spots).
1
1
1
1
0.8
0.6
0.6
0.6
0.6
0.6
0.6
0.4
0.4
0.4
0.4
0.4
0.2
0.2
0
0
-0.2
-0.4
0
0.2
0.4
0.6
r/R
0.8
1
-
0.2
0.2
0
-0.2
-0.2
-0.4
-0.4
0
0
0.2
0.4
0.6
r/R
0.8
1
Ez/Emax
0.8
F/Fmax
0.8
Ez/Emax
0.8
F=-
F/Fmax
0.8
0.8
Ez/Emax
1
0.4
-
0.2
0.2
0
-0.2
-0.2
-0.4
-0.4
0
-0.2
-0.4
0
0.2
0.4
0.6
r/R
Field distributions of 3, 6, and 9 GHz modes and corresponding Miller force
Green spots are unstable equilibriums.
0.8
1
F/Fmax
1
1
0.8
s
F=-
F/Fmax
0.6
1
0.4
0.2
0
-0.2
2500 eV
50 eV
-0.4
W
Secondary emission coefficient
0
0.2
0.4
0.6
0.8
1
r/R
Full Milller force of 3,6, and 9 GHz modes
H
Hr
Beam channel
Trajectories of primary and
secondary electrons
Ez
Secondary electrons are
able to be born at side
wall.
Initial energy 3-5 eV.
All trajectories of electrons due to the resulting Miller force go to the side wall.
Assume that these electrons cause secondary electrons. Do secondary electrons
produce next generation of particles? So, let us investigate multipactor threat at side
wall.
1
1
0.75
0.75
0.5
H/Hmax, a.u.
E/Emax, a.u.
0.5
0.25
0.25
0
4
1
-0.25
2
0
-0.5
-0.25
-0.75
3
-1
-0.5
0
60
120
180
240
300
0
360
60
0.015
1
y, cm
0.01
2
3
0
-0.005
240
300
360
Full magnetic field at side wall
Full electric field of 3,6, and 9 GHz modes in the
center of cavity
0.02 Side wall
0
180
Phase, grad
Phase, grad
0.005
120
0.002
0.004
0.006
0.008
0.01
x, cm
4
-0.01
Trajectories of electrons started at side wall
120
150
100
125
80
100
We, eV
We, eV
3 modes
1 mode
60
75
40
50
20
25
0
0
0
60
120
180
240
Phase, grad
300
360
100
200
300
400
500
E, MV/m
Energy of incoming to side wall electrons
Maximum energy of incoming electrons at
as a function of field phase under E=370 MV/m side wall In dependence on full electric field
for single mode TM010 cavity and for three
in the center of cavity (3 modes)
mode cavity TM010, TM020, TM030.
At 370 MV/m there are electrons which gather about 100 eV energy before to drop
on side wall. Such electrons are able to born secondary electrons with
reproduction more than 1!
H
0
Ez
120
120
100
100
1
y
120
0.75
100
60
60
40
40
20
20
0
0
0
120
240
360
480
600
720
Phase, grad
Energies of secondary electrons incoming to side
wall and trajectories of most energetic electrons
E=370 MV/m
80
0.25
0
60
-0.25
40
-0.5
Distance Y, 10-3 mm
80
H/Hmax, a.u.
80
Distance Y, 10-3 mm
We, eV
0.5
20
-0.75
-1
0
0
120
240
360
480
600
720
Phase, grad
Full magnetic field of 3,6, and 9 GHz modes at
side wall and trajectories of secondary electrons
E=370 MV/m
Most dangerous high energetic electrons (with W100 eV) finish its paths at
similar field phase (when magnetic field reaches maximum).
The secondary electrons born in this phase can not gather enough high energies
in order to provide growth of electron concentration.
There’s a better way to do it. Find it!
Thomas Edison
Raise of breakdown threshold in asymmetric cavity
a)
b)
U
U
Anode
Cathode
Cathode
Anode
The DC voltage is the same in both cases, nevertheless in case (a) breakdown
threshold is bigger than in case (b)!
cavity
Instant field
e-emission
is impossible
E-field
e-emission
is possible
e-bunch
At RF field electron emission is impossible, if E-field pushes electrons in a wall.
In a single mode cavity this fact means nothing, because RF field oscillates exactly between
+maximum and –maximum. “Cathode” and “Anode” replace each other for a half of period.
In a multi-mode cavity situation is quite different!
Let us consider a cavity having two axisymmetric modes at frequencies f1 and f2 respectively:
“Anode”
“Anode”
Ez
Right wall
Left wall
E0
“Cathode”
Field on the left wal
The field on the right wall oscillates between +E0
and –E0 and never exceeds E0 by module. The
field on the left wall has maximum +2E0 and
minimum -E0 correspondingly.
But +2E0 is actually “anode” field.
So, if breakdown threshold exactly equals E0,
then the accelerating gradient is asymptotically
1.4 E0!
0
L
Longitudinal field distribution of the symmetric
mode at frequency f1
Ez
E0
0
L
Longitudinal field distribution of the asymmetric
mode at frequency f2=2f1
All wish to possess knowledge, but few, comparatively
speaking, are willing to pay the price.
Juvenal
Preparation and time schedule
In order to start experiment (in case of your approval) we will have:
1. To finish necessary calculations (results to be confirmed by you).
2. To calculate beam optics (quadrupole doublets).
3. To coordinate pumping and flanges.
4. To produce and to test cavities, to produce doublets.
5. And to solve all administrative problems (money, manpower etc)…
So, if all these steps will be done, the experiment start could be not earlier than
the end of 2010.
Many ideas grow better when transplanted into
another mind than in the one they sprung up.
Holmes
e+
eaccelerated
beam
accelerated
beam
Lb /2
e-
e-
Lb
drive beam
Two-beam two-sections accelerating structure with aspect ratio 1:2
drive beam
Summary
1. The proposed multi-mode experiment to raise RF breakdown
threshold is able to help in understanding of fundamental nature
of this phenomena.
2. CTF3 seems to be the most comfortable and powerful tool. Beam
optics of CTF3 can be adopted for purposes of experiment.
3. Two kinds of experiments are considered:
- with axisymmetric cavities having modes with symmetric
distribution (the expecting threshold raise is ~1.3),
- with axisymmetric but longitudinally asymmetric modes (the
expecting threshold raise is about 2).
4. Preliminary analysis shows that pulse heating and multipactor
phenomena do not spoil experiment aims.
5. Methodology implies comparison of breakdown probability in 1-,
2-, and 3-mode cavities under the same E-field level and possibly
visual observation of breakdown insight cavities.
6. Start of experiment could be in the end of 2010 - beginning of
2011.