Download RF systems for Particle Accelerators II

RF Systems for Particle Accelerators II (Pages 163-176)
Acceleratings structures for linacs
Klystrons as power generators for accelerators
The klystron modulator
Magnetrons
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Acceleratings structures for linacs
In LINACS cylindrical waveguides are sucessfully used for acceleration.
The generated TM01 mode has a longitudinal electric field Ez with a maximum along the axis. For loss-free wave
propagation lz > l in free space and that means that the phase velocity within the waveguide is greater than speed of
light. The phase velocity of the wave has to be reduced vf  c, in order to use these devices for acceleration.
Particles travelling slowly than speed of light undergo acceleration from the passing wave for half a period but then
experience an equal deccelaration. Averaged over long time interval there is no transfer of energy to particles.
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The phase velocity of the wave vf has to be matched to the velocity of the particles for energy transfer over long
sections.
Iris-chaped screens installed at constant separation distance reduces the phase velocity to vf c. This is a ”discloaded structure”
The relation between wavenumber kz and frequency w:
(5.20)
This curve always lies in the region vf  c.
Installation of irises allows the curve to flat off and cross the boundary line vf = c, at point kz =/d. Above this value
vf  c, and particle acceleration is possible. Choosing d, vf can be set to any value.
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In the beginning of Linacs the irises are arranged very close, since particles still have non relativistic velocities  =
v/c<<1. The phase velocity, vf is matched to the velocity of accelerated particle ( matching) by continously
increasing d.
Once particles reach speed of light, waveguide structure with constant iris separation are used.
The Standard operation of Linac is in S band:l=0.1m (fRF =2.998 GHz).
Rf power is provided by pulsed power tubes, klystrons, and feeded into linac by means of a TE10 wave in a
rectangular waveguide. At interface the rectangular TE10 waveguide is connected perpendicular to the cylindrical
TM01 cavity. Both waves have the same configuration at the interface. The wave is able to pass easily from one mode
to the other. Because of no completely identical geometry, some reflections must be compensated by a coupling slot.
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Linac structures can operate in travelling wave mode and in standing wave mode. The difference is if the structure is
closed by a reflecting boundary or not.
1. Travelling wave: an absorber is used to avoid reflections, connected through a coupler and leading the wave out.
The solution of the wave equation yields only a travelling wave.
2. Standing wave: The wave is reflected with no losses and overlaps the incomming one to produce the standing wave.
In smooth waveguides, waves with a wide range
of frequencies can propagate without losses
(l<lc).
The irises form a periodic structure within the
cavity reflecting the wave as it passes through
and causes interference. Loss-free wave
propagation can only ocurr if the wavelenght is
an integer multiple of the iris separation d:
(5.44)
(5.45)
Irises only allow certain wavelengths
characterized by number p to travel in
longitudinal direction. These fixed wave
configurations are termed modes.
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For acceleration only a few modes are used:
(5.46)
The -mode requires relatively long settling time (It
takes long time for transients oscillations to die away
and stationary state to be reached). Not suitable for fast
pulsed operation.
The /2-mode has a relatively low shunt impedance
per unit length. For fixed RF power the energy gain per
structure is rather small
The 2/3-mode, is the best compromise, It has short
settling time and high shunt impedance (prefered in
modern linacs).
The energy gain of a particle travelling a distance ”l ”through the structure depends on the potential difference ”U”
crossed by the particle:
(5.47)
PRF is the supplied RF power, r0 is the shunt impedance per meter, K is a korrection factor (K≈0.8).
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Some exemples: The shunt impedance per metre can be stimated by the empirical formula:
(5.48)
Where, z =vf /c, is the phase velocity; h=h/d, (h- thickness, d- iris separation); p- number of iris per wavelength (mode
number); D=[2 (1-h) ]/p.
Stanford Linear Accelerator Centre (SLAC ). The Length of the linac 3000 m; 2b=82.474 mm; 2a=22.606 mm;
h=5.842 mm; d=35.001mm. For z =1; in 2 /3-mode (p=3), the shunt impedance per metre of the SLAC structure:
The total accelerating voltage (l=3m) for PRF=35MW, is 59.7 MV. Such power can be maintained only in pulse operation
(few ms), because of the heating.
The linac structure must be operated at a well defined temperature: DT=+/-0.1o . It is not technically feasible to align
individual cells during operation. The gradiant, energy gain per metre in the SLAC structure is:
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Klystrons as power generators for accelerators
Cavities in circular accelerators and linacs require RF power
of some tens of kW and as much as several MW in large high
energy accelerators or linacs.
Klystrons are effective power generators for acceleration
applications.
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In the klystron, electrons are emitted from a round cathode with large area and they are accelerated by a voltage of
tens of kV (From few A to more than 10 A). Suitable shaped electrodes near cathode are used to focus the beam.
Collimation is reached by means of several solenoids along the tube.
The electron beam coming out from cathode with a well
defined particle velocity passes through a first cylindrical
cavity operating in TM011 or TM012 , in order to achieve a
better coupling to the beam.
An external preamplifier excites a wave in the first
resonator of tens of watts. The field excited by this wave will
accelerate, brake or not influence the particles, depending
on the phase. The velocity of the electrons passing through is
modulated with a frequency equal to resonance frequency.
In zero field particles will drift, the faster ones move ahead and slower ones lag behind.
After certain distance particles will be bunched. The continuous current from the cathode
become pulsed with a frequency equal to frequency of the coupled driving supply.
The second cavity is resonantly excited by the pulsed current. The generated RF wave is
coupled out (The kinetic energy stored in the beam is transformed into RF energy).
The output power of the klystron can be computed in the form:
(5.49)
U0 - supply voltage of klystron, Ibeam -beam current, h – efficiency of klystron (45%-65%).
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A typical accelerator klystron of average power operates at voltage of U0=45kV, a beam current of Ibeam=12.5A and
efficiency of h=0.45. The resulting HF power Pklystron=hU0Ibeam=253kW.
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Voltage, Uo [kV]
Beam current, Ibeam [A]
Efficiency, h
Pklystron [kW]=hIbeamUo
Pulse
length
ms
Typical klystron
45
12.5
0.45
253
CW
Klystrons driving
linacs, f=2.998 GHz
250-300
250
0.45
30000-35000
few
Now, it is possible to get peak values of up to 1.2MW per tube in continous wave mode, in the frequency range of 350500MHz.
A better coupling of the beam to output cavity is achieved by inserting two or more cavities tuned to frequencies close
to the operating one
In the relativistic Klystron (electrons travel at
relativistic velocities), due to high beam current of
several thousands amperes, inductive accelerating
sections are used. They consist of a single winding
around a ferrite core. They have low impedance.
Using strong pulse currents a voltage of a few
hundred kV is generated, which accelerates the
particles as they cross. A whole serie of inductive
accelerating sections needs to achieve the final
energy.
The electrons are further accelerated by a series of
inductive accelerating sections in order to
compensate for losses in output power.
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The electrical power used by high power klystrons in storage rings comes from power supplies regulated by thyristors
which provide a constant high voltage.
Klystrons Modulators. For linac klystrons operating in pulsed mode a voltage of up to 300 kV and a current of around
250 A must be supplied for a period of a few ms, that means a pulse power of up to 80 MW. S-band klystrons with this
level of power use power supplies called klystron modulators.
Short pulses of high power are
produced by charging capacitors up
to high voltages and then using a
suitable switch to discharge them
through a very low resistance load.
The energy required: W=Pkttot for
the input power of the klystron Pk ,
with a pulse duration of ttot . The
energy is stored in C1, C2,…,Cn of
the pulse formed network (PFN)to a
voltage UL.
A PFN formed by capacitors and
inductors , when discharging form a
rectangular pulse. The sharpness of
pulse edges increases with more LC
elements in the chain. Individual
values of L anc C are smaller.
The energy stored in a PFN:
(5.50)
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The total capacitance follows:
(5.51)
Computing the other parameters of the PFN, the inductance Li : when discharging the PFN the current pulse flows
through a load RL (real). For optimal energy matching the load which terminates the chain must match its impedance Z0.
(5.52)
RL has exactly half the load voltage, UL/2, across it. The power delivered to the load is:
(5.53)
The total inductance (5.52):
(5.54)
The transit time along the PFN, tPFN
(5.55)
The PFN is discharged by a thyratron (a gas discharge tube which can switch voltages of several tents of kV and
currents of several kA). It is triggered by sending a pulse to the control grid (<ms). The current discharged from the PFN
flows through the load RL (primary coil of a pulse transformer, 4-6 windings). The transformer has two identical coils as
secondaries. The high voltage for the klystron heating is supplied via these two windings (70 windings). An additional
filament transformer is used in order the secondary windings not to carry to high filamente current.
The secondary side of pulse transformer is at high voltage (300kV), that´s why this side is placed in an oil-filled tank.
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Resonant charging of the PFN. The power supply generates only half of charging voltage: U0=UL/2. An inductance L is
conected between the power supply and the PFN (L>>Li). Capacitances are aproximately connected in parallel, because
of small Li. Ctot is the load of the PFN. The voltage in Ctot depends on charging current:
(5.56)
The supply current flows through L, with ohmic losses characterizes by Rv connected in series with the inductor.
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Using that x (t)= I(t)dt, the equation that describes the charging process:
(5.57)
This inhomogeneous equation has the solution:
(5.58)
Assuming slight damping z<<w0, the initial conditions yields:
Uc(0)=0

U`c(0)=0
 B=0
A=-U0
For this virtually undamped oscillator the voltage in the capacitors has the form:
(5.59)
Half an oscillation period after discharge of PFN, the voltage on the capacitors reaches maximum value Umax=2U0 . The
diode connected in series with L prevents the oscillation from continuing and discharging the PFN again.
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The magnetron is called a "crossed-field“, because both magnetic and electric fields are employed in its operation, and
they are produced in perpendicular directions so that they cross. The applied magnetic field is constant and applied
along the axis of the circular device illustrated. The power to the device is applied to the center cathode which is heated
to supply energetic electrons which would, in the absence of the magnetic field, tend to move radially outward to the
ring anode which surrounds it.
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Electrons are released at the center hot cathode by the process of thermionic emission and have an accelerating field
which moves them outward toward the anode. The axial magnetic field exerts a magnetic force on these charges which is
perpendicular to their initially radial motion, and they tend to be swept around the circle. In this way, work is done on
the charges and therefore energy from the power supply is given to them. As these electrons sweep toward a point where
there is excess negative charge, that charge tends to be pushed back around the cavity, imparting energy to the
oscillation at the natural frequency of the cavity. This driven oscillation of the charges around the cavities leads to
radiation of electromagnetic waves, the output of the magnetron.
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