Transcript Lecture 7 Normal conducting RF

Lecture 5 Normal
conducting RF
Dr G Burt
Lancaster University
Engineering
Copper Cavities
2
1V
R
2 Pc
In copper cavities the shunt impedance, R, should be
maximised in order to achieve a high accelerating gradient.
Normal conducting cavities require nosecones and a small
beam pipe in order to increase the shunt impedance factor
Cavity Body
Temperature Probe
Directed Water Flow
into Cavity
Water Flow
out of Cavity
T
Average Heating
• In normal conducting cavities, the RF deposits large
amounts of power as heat in the cavity walls.
• This heat is removed by flushing cooling water through
special copper cooling channels in the cavity. The faster
the water flows (and the cooler), the more heat is
removed.
• For CW cavities, the cavity temperature reaches steady
state when the water cooling removes as much power as
is deposited in the RF structure.
• This usually is required to be calculated in a Finite
Element code to determine temperature rises.
• Temperature rises can cause surface deformation,
surface cracking, outgassing or even melting.
• By pulsing the RF we can reach much higher gradients
as the average power flow is much less than the peak
power flow.
Pulsed Heating
Pulsed RF however has problems due to
heat diffusion effects.
Over short timescales (<10ms) the heat
doesn’t diffuse far enough into the material to
reach the water cooling.
This means that all the heat is deposited in a
small volume with no cooling.
Cyclic heating can lead to surface damage.
Field Enhancement
• The surface of an accelerating
structure will have a number of
imperfections at the surface
caused by grain boundaries,
scratches, bumps etc.
• As the surface is an
equipotential the electric fields
at these small imperfections
can be greatly enhanced.
• In some cases the field can be
increase by a factor of several
hundred.
10000
Beta
Elocal=b E0
100000
1000
100
10
2b
1
1
10
100
h/b
h
1000
Field Emission
• As we saw in Lecture 3, high electric fields can lead to
electrons quantum tunnelling out of the structure creating
a field emitted current.
Once emitted this field emitted
current can interact with the
cavity fields.
Although initially low energy, the
electrons can potentially be
accelerated to close to the
speed of light with the main
electron beam, if the fields are
high enough.
This is known as dark current
trapping.
Breakdown
• Breakdown occurs when a
plasma discharge is generated in
the cavity.
• This is almost always associated
with some of the cavity walls
being heated until it vaporises
and the gas is then ionised by
field emission. The exact
mechanisms are still not well
understood.
• When this occurs all the incoming
RF is reflected back up the
coupler.
• This is the major limitation to
gradient in most pulsed RF
cavities and can permanently
damage the structure.
Kilpatrick Limits
• A rough empirical formula for the peak surface electric
field is
• It is not clear why the field strength decreases with
frequency.
• It is also noted that breakdown is mitigated slightly by
going to lower group velocity structures.
• The maximum field strength also varies with pulse length
as t-0.25 (only true for a limited number of pulse lengths)
• As a SCRF cavity would quench long before breakdown,
we only see breakdown in normal conducting structures.
RF Conditioning
• As a cavity is often manufactured with a number of
nucleation sites for breakdown it is necessary to
condition the cavity.
• This consists of a number of semi-controlled RF
breakdowns, caused by increasing the RF power or
pulse length very slowly over a number of days/hours.
• This causes vaporisation of the nucleation sites (sharp
points) just above the breakdown threshold causing a
minimum amount of damage.
• In theory this should allow the structure to be conditioned
to any gradient but in practice every structure has a
maximum field at which processing fails to be effective.
• This is likely to be due to the production of secondary
nucleation sites after melting the primary sites.
Maximum Gradient Limits
• All the limiting
factors scale
differently with
frequency.
• They also mostly
vary with pulse
length.
• The limiting
factor tends to
be different from
cavity to cavity.
Nose Cones
If we decrease the accelerating gap, while keeping the same
voltage between the gap, the effective accelerating voltage
increases due to the transit time factor.
 L / 2

V     Ez  z, t  ei z / c dz   Ez 0 LT cos t 
 L / 2

Cavity Body
Temperature Probe
Directed Water Flow
into Cavity
Water Flow
out of Cavity
As the gap is smaller the field strengths
increase, which is good where the beam
is but bad elsewhere.
T
To avoid problems we only decrease the
gap near the beam. The narrowed gap
region is known as a nose-cone.
RFQ
Radio frequency Quadropoles are
electrostatic quad’s for focussing the
beam.
If the electrodes are specially shaped
they can also accelerate the beam.
This is especially useful for low energy
beams where space charge forces are
large.
Standing Wave Cavities
The most common type of
structure is the p mode
standing wave structure.
This can be a single cell or
multiple cells coupled
together.
These structures cannot have too many cells per cavity and means that for high
energy accelerators many couplers are required. The cost of this is why these
structures are overlooked for linear colliders like CLIC and NLC.
Phase Advance
• Not all cells in a multi-cell
structure will have the
same phase.
• The phase difference
between two cells is
known as the phase
advance.
• In a travelling wave
structure the phase
advance is the axial
wavenumber multiplied by
the iris spacing (f=kzL)
• An iris loaded structure
will have a group velocity
of zero (standing wave) at
phase advances of 0 and
p.
Pi/2 structures
9.7
Frequency, GHz
9.6
fc=9.3 GHz, fa=9.5 Ghz
9.5
"
9.4
fc=fa=9.3 GHz
9.3
"
9.2
fc=9.3 GHz, fa=9.2 Ghz
9.1
"
9
8.9
0
15
30
45
60
75
90
105
120
135
150
165
180
Phase, deg
A mode with a 90 degree phase advance has the largest frequency gap
between neighbouring modes for a given cell-to-cell coupling.
This makes the cavity mores stable to manufacturing, or RF source errors.
If we use this mode then every 2nd cavity is empty which is inefficient.
Hence we use a bi-periodic cavity where each 2nd cavity is smaller
Side coupled cavities
• For multicell cavities a
small aperture leads to low
coupling between the
cavities.
• This causes there to be
very small frequency
separation between
modes.
• In order to increase the
cell-to-cell coupling we can
use a side cavity.
• We then use a p/2 mode,
where the side cell has low
fields.
Bi-periodic cavity
p-mode
high shunt
impedance
p/2-mode
high field
stability
p/2-mode
bi-periodic
both !
L
It’s a conventional p/2-mode cavity where alternate cavities are contracted to occupy less space,
hence
1. Beam sees a p-mode high acceleration
2. RF sees a p/2-mode field highly stable
Accelerating cavity
Coupling cavity
Lap
b = 0.28 0.48
0.68
0.88
1
1
1
17
KeV
40
20
0
Phi, deg
0
1
2
3
4
5
6
-20
-40
focusing
-60
-80
bunching
-100
Ce ll
7
8
Travelling wave structures
• Normal conducting cavities can
be standing wave or travelling
wave.
• In TW structures the waves
phase velocity, is equal to the
speed of the particles to be
accelerated.
• The beam will see the same
phase throughout the
structure.
• Power can flow through all the
cavities and out the other side,
very low Q.
• Power is also dissipated in the
cavity walls.
Iris loaded structure
As we saw in lecture 1, a
smooth waveguide cannot be
used for accelerating particles
as the phase velocity is always
greater than c.
To obtain useful acceleration we must
slow down the waves phase velocity.
In accelerators we do so by using periodic
iris loading.
The reflections at each iris interfere with
each other altering the dispersion of the
structure.
The dispersion becomes sinusoidal
instead of parabolic.
Matched Couplers
•In order for the
structure to contain a
travelling wave we
must ensure that
there are low
reflections at the
input and output
couplers.
• This is not the same as S11=0 as the reflected power at one coupler
could be cancelled by reflections at the other coupler, while
containing a standing wave in the cavity.
• In order to verify a structure is matched we must measure the fields
inside the cavity.
Floquet Theorem
1
0.75
R
By measuring how the field varies between
a cell and its nearest two neighbours we
can use Floquet theorem to calculate the
phase and reflections
0.5
0.25
0
0
10
20
30
40
50
60
70
z [mm]
E = field
P = cell length
R = reflection coefficient
y = required phase advance
Phase advance per cell [deg]
160
140
122.4
120
100
80
0
10
20
30
40
z [mm]
50
60
70
Measuring Phase Advance and
Match
Wakefields
• For X-band structures the beampipe must be very small
in radius, r, to remain cut-off to the operating mode.
• The short range transverse wakefield of a cavity scales
roughly with r3 (depending on the structure).
• The short range wakefield cannot be damped so the
structure alignment must be very precise to avoid
transverse offsets.
• There is a method of defeating short range wakes,
known as BNS damping.
• Here the electrons in the head and tail of the bunch have
differing betatron wavenumbers. This can create a
situation where the wake of the head periodically drive
the tails oscillation and then to cancel it. (See R. Jones
lectures for more details)
Cell Manufacture
Specification is 5 mm. This is
the best that can be achieved
using CNC milling or lathe.
A poor surface roughness
can lead to breakdown. The
machining must produce a
good surface finish.
Cavity Joining
Having manufactured the cells they then must be
assembled to a similar precision using vacuum
brazing or diffusion bonding. The joining must
provide good clean intersections with a good
alignment.