A Millich
22-Feb-2001
High R/Q PETS for 30 GHz power production with CTF3
linac beam before recombination (revisited):
Power output from the PETS:
ls 2  qb 
 
P
2c  Tb 
2
 R '  1
 
 Q  
  g
 2
 F  


Power output is linear with R/Q but varies as the second
power of beam current, which appears as the ratio of bunch
charge over bunch interval.
Six-waveguide PETS nominal parameters for CTF3:
Taking into account the reduced beam current in CTF3 with
respect to CLIC, the four-waveguide PETS has a beam
aperture of 24.mm. Its main parameters are:
R'/Q= 48. /m (circuit convention)
 g = 0.41 normalised group velocity of 2/3 mode
The nominal power output for a beam current of 35 A, after
recombination is:
P= 423. MW for a structure 1 meter long, neglecting
losses.
Before recombination the current is ten times lower than
after, so that the power output is one hundred times lower.
We can only partially compensate this factor 100 by
increasing the R'/Q of the PETS.
We shall assume that the structures have length: ls  1. m
The four-waveguide PETS with reduced aperture
One possible way to increase the output power is by using
the four-waveguide PETS with reduced aperture of 15.mm:
R'/Q= 540. /m (circuit)
 g = 0.53
P= 3.7 MW for I=3.5 A and with the same assumptions as
above.
This structure already exists and will be used in CTF2 this
year.
By further reducing the beam aperture to 10 mm,
the four-waveguide PETS will have the following parameters:
R'/Q= 1763. /m (circuit)
 g = 0.46
P= 13.7 MW for I=3.5 A and with the same assumptions as
above.
This type of structure can be built using the same
construction and assembly methods as the existing PETS.
Cylindrical PETS with reduced aperture.
For the same beam aperture the highest R/Q is obtained
with the cylindrical symmetric PETS. By reducing the beam
aperture diameter to 10 mm we get the following
parameters:
R'/Q = 2190. /m (circuit convention)
 g = 0.46 normalised group velocity of 2/3 mode
P= 17. MW for I=3.5 A and neglecting form factor and
losses.
This type of structure presents two new features:
- it can be built using the a novel construction method which
makes use of electro-forming to deposit a copper layer on
top an aluminium substrate, which is consequently
removed by chemical means and
- its output couplers are of a new design.
Conclusion:
it appears that the power delivered by the highest
impedance PETS which can conceivably be built is not
sufficient for meaningful 30 GHz power production before
bunch recombination in CTF3. This of course does not
exclude the possibility to improve the situation by power recirculation or other exotic methods.
Peak Electric and Magnetic Fields in PETS as function of
output power
It is interesting to compute the peak values of the fields in
the PETS described above for a peak output power of say
100 MW, in case of use with the full beam current after
recombination.
The formula relating the average decelerating electric field in
PETS to the output power P is [1]
R' 
Ez  2P
Q vg
(1)
R'
where
is the normalised shunt impedance expressed in
Q
circuit Ohm/m,  and v g are respectively the decelerating
mode angular frequency and its group velocity.
For the particular case of the four-waveguide PETS with
R'
aperture 15 mm,
 540 / m , vg  0.53  c , assuming an
Q
output power of 100 MW,
the average decelerating field is 11.3 MV/m.
Using a three-cell model of the 15 mm aperture PETS in
MAFIA we obtained the electric field map in the case of
standing wave mode from which we could compute the ratio
of peak electric field near the teeth to the average
decelerating field on the axis of the structure. This ratio
turned out to be 9.5 for the 2/3 travelling wave mode.
Consequently the peak electric field in the 15 mm aperture
four-waveguide PETS is
E p = 107 MV/m for 100 MW output power.
The dependence being quadratic, doubling the power would
increase the peak field to 151 MV/m.
The peak magnetic field for 100 MW output power is found
to be
H p  1.68  105 A/m.
For the six-waveguide PETS with 24 mm aperture,
R'
 48 /m and vg  0.41c , the ratio peak to effective
Q
average decelerating field is 19.
The average field computed with (1) gives:
E=3.84 MV/m for an output power level of 100 MW.
Consequently the peak electric field for this PETS is
E p =73 MV/m at 100 MW output power level.
The peak magnetic field is
H p  1.28  105 A/m.
For the cylindrical PETS with 10 mm aperture,
R'
 2190. / m and vg  0.46c , the peak electric and
Q
magnetic fields are respectively:
E p = 82. MV/m and
H p  1.4  105 A / m
for an output power of 100 MW.
These peak field levels are quite conventional and should
not represent a danger for the structure inner surfaces.
However there are critical spots just before the entrance of
the output waveguides where the fields may exceed the
above values. This matter is being investigated in view of
recent experimental evidence.
[1] A.Millich, L.Thorndahl, CLIC Note 407.