CERN European Organization for Nuclear Research European Laboratory for Particle Physics

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1 CERN European Organization for Nuclear Research European Laboratory for Particle Physics CLIC Note 592 CERN-OPEN /06/2004 HIGH-POWER MICROWAVE PULSE COMPRESSION OF KLYSTRONS BY PHASE-MODULATION OF HIGH-Q STORAGE CAVITIES R.Bossart, P.Brown, J.Mourier, I.V.Syratchev, L.Tanner Abstract At the CERN linear electron accelerators LIL and CTF, the peak RF power from the 3GHzklystrons was doubled by means of LIPS microwave pulse compressors. To produce constant RF power from the cavity-based pulse compressors, the klystrons were driven by a fast RF-phase modulation program. For the CLIC Test Facility CTF3, a new type of a Barrel Open Cavity (BOC) with a high quality factor Q 0 has been developed. Contrary to LIPS with two resonant cavities, BOC operates with a single cavity supporting two orthogonal resonant modes TM 10,1,1 in the same cavity. For both LIPS and BOC storage cavities, it is important that the RF power reflected back to the klystron is minimal. This implies that the resonant frequencies, Q-factors and coupling factors of the two resonant modes of a pulse compressor are closely matched, and that the resonant frequencies are accurate to within a few KHz. The effects of small differences between the two orthogonal modes of the BOC cavity have been investigated. The dynamic pulse response of a klystron and LIPS pulse compressor has been measured for fast phase modulation. The high power tests have demonstrated that the compressed RF power was doubled and reached 70 MW during 1.5 µs. The power amplitude was stabilized to within ±1% by the feed-forward phase correction program, and the measured phase sag of the compressed output pulse was 8, as predicted by the theory. Geneva-Switzerland 14 June 2004

2 1 Historical Background of LIPS Pulse Compression At LIL, the LEP Injector Linac, the energy gain provided by the accelerating RF sections was doubled by means of the LIPS pulse compressors installed at the output of the RF power klystrons 1. The LIPS pulse compressor consists of two RF storage cavities connected by a hybrid power combiner, Fig.1-2. The cavities store the RF energy of the klystron and release it to the acceleration sections in a very short time before the end of the RF pulse of the klystron. The klystrons produce a 3 GHz pulse of MW power lasting for 5 µs. As the duration of the RF pulse of the klystron is several times longer than the filling time of the accelerating sections and the duration of the electron beam, it is possible to compress the RF energy by the LIPS cavities into a short RF pulse of 1.5 µs duration and 70 MW average power. In order to produce a compressed RF pulse with constant peak power amplitude, A. Fiebig and Ch. Schieblich have proposed to modulate the RF-phase of the 3 GHz signal at the klystron input by a fast phase modulation program 2. The phase modulation technique avoids the large, short power peak followed by an exponential decay of the SLED pulse compression technique 3. In order to minimize the RF losses in the LIPS cavities, an overmoded cylindrical resonator TE 038 with a quality factor Q 0 = ± was constructed. For optimum energy gain in LIL, the coupling factor of the LIPS cavities was β = 8±1. Each cavity was connected to the waveguide by a pair of coupling holes, which strongly damp all parasitic dipole modes of the cavity 1. Each LIPS cavity has a mobile tuner that allows the resonant frequency to be adjusted with a resolution of 1 KHz. The fine frequency tuning facility of the LIPS cavities has proven to be very useful during LIL operation, minimizing the reflected power towards the klystrons and improving the shape of the compressed RF output pulses. The fine frequency adjustment of the LIPS cavities also allowed compensation of small amplitude and phase errors between the two cavities and the hybrid power coupler, so that the recombination of the two orthogonal waves from the two resonators with slightly different coupling factors could be adjusted for maximum power gain and minimum reflection. The resonant frequency of a pair of LIPS cavities could be easily matched to less than 2 KHz by minimizing the RF power at the zero crossing of the pulse response PLI(t) of a LIPS assembly, see photo Φ2 of Fig.3. During the pulse compression for constant output power, the phase error of the compressed RF pulse was minimized by offsetting the LIPS frequency ~130 KHz from the accelerator frequency. A linear phase ramp corresponding to this frequency offset was included in the phase modulation program, compensating the linear phase error of the pulse compression. 1 A.Fiebig, R.Hohbach, P.Marchand, J.O.Pearce, Design considerations, construction and performance of a SLEDtype RF pulse compressor, 1987 Particle Accelerator Conference, Washington, 1987, p A.Fiebig and Ch.Schieblich, A SLED type pulse compressor with square pulse shape, Proc. of European Particle Conference, Nice, 1990, p Z.D.Farkas, H.A.Hogg, G.A.Loew, P.B.Wilson, SLED: A method for doubling SLAC s energy, Proc. of 9 th Int.Conf. on High Energy Accelerators, SLAC Stanford, 1974, p.576.

3 2 Tests carried out with a klystron and a LIPS pulse compressor at LIL in December 2000 have shown that the feed-forward control method of the phase modulation at the klystron input provided a perfectly constant power output of 54 MW during 1.5 µs from the LIPS cavities driven by a klystron power of 28 MW during 5.0 µs. The power amplitude of the compressed RF pulse could be stabilized to better than P/P < ±1% in spite of a klystron power ripple larger than ±3%, see photo Φ2 of Fig.3. However, the RF phase at the LIPS output has varied by ϕ = 8 over 1.4 µs during the pulse compression, in perfect agreement with the analytical simulation program based on the differential equations of the transient response of the RF amplitude and phase of the LIPS cavities 2. The Barrel Open Cavity BOC Measurements on the Cold Model In order to reduce the cost of the additional RF pulse compressors required for CTF3, a single Barrel Open Cavity 4 (BOC) has been developed with two orthogonal 3 GHz resonance modes TM 10,1,1(number of periods in spherical coordinates ϕ,δ,r). The mechanical layout of the cold model of BOC is shown in Fig.4. The advantage of the BOC design is that only one cavity is needed, whereas for a SLED type pulse compressor two cavities are required to avoid power reflection towards the klystron. In the over-moded, quasi-spherical BOC cavity, two orthogonal field modes coexist at the same frequency. The various RF parameters of LIPS and BOC are given in Fig.5. At the beginning of the LIPS development, a spherical resonator was tested, but was soon abandoned due to the many parasitic resonances close to the nominal resonant frequency 5. For the BOC design, the multiple modes of spherical resonators have been avoided by choosing different curvature radii for the cavity wall in the horizontal equator plane ϕ and in the vertical plane δ from pole to pole. Moreover, the pole areas have been equipped with removable flat covers for vacuum pumping. These geometric asymmetries and the selectivity of the multi-hole coupler have strongly damped many of the parasitic spherical modes. The BOC therefore has an excellent frequency separation of more than 35 MHz between the nominal frequency 3 GHz and the nearest parasitic modes, Fig.6. The resonant frequency of the cold model BOC was 3007 MHz, some 9 MHz above the nominal frequency. Unfortunately, even with a tuning plate added to the cover of the barrel cavity, it was not possible to correct the resonant frequency by more than 1 MHz. RF measurements revealed that a tuning plunger would be inefficient, and would cause important RF losses, reducing the quality factor of the cavity. The losses at the covers have been reduced in the next design of BOC by reshaping the cavity geometry. To correct the resonant frequency, the diameter of the new barrel cavity has been increased. Since there is no possibility to tune the resonant frequency otherwise than at the equator of the barrel open cavity, the cavity diameter must be machined with utmost precision, and the exact resonant frequency required for operation must be tuned by regulating the temperature of the cooling water in the range 30 ± 5 C, providing a fine 4 P.Brown, I.Syratchev, 3 GHz Barrel Open Cavity (BOC) RF pulse compressor for CTF3, CERN-Preprint (in preparation). 5 A.Fiebig and R.Hohbach, Study of peak power doublers with spherical resonators, Proc. of 1983 Particle Accelerator Conference, Santa Fe, 1983.

4 3 adjustment of the resonant frequency over the range ± 0.25 MHz for the cavity under vacuum. The theoretical Q-factor of a copper BOC cavity is Q 0 = For the cold model BOC, however, the unloaded Q-factor was only Q 0 = ± Probably, the RF losses of the RF contacts at the two covers on each side of the barrel cavity were larger than expected and not reproducible. There was also an unexpected parasitic resonance at 1 MHz above the nominal resonance. Since this parasitic mode had a field component along the pole-to-pole axis, it could be damped by a SiC-absorber mounted on the inside of the covers. Another feature of the BOC is the multi-hole coupling between the waveguide and the cavity. The waveguide runs around the cavity in the equatorial plane and has 39 coupling holes with a diameter of ~13mm drilled between waveguide and cavity, at a distance of λ g /4 between holes, Fig.4. For two exactly orthogonal resonant modes in the BOC cavity, the λ g /4 multi-hole coupler provides good directivity, so that very little RF power should be emitted backwards to the klystron. During the RF pulse compression, all the RF power reflected by the cavity is transmitted forwards to the accelerating sections, due to the forward directivity of the coupler. Theoretically, no power is reflected back to the klystron, if the two modes of the BOC cavity are equal in amplitude and orthogonal in phase. However, there was a strong return loss S11= -13 db measured at the input port 1 of the cold model BOC terminated by a matched load at the output. As a possible cause of the strong return loss, mismatches between the coupler waveguide and the WG-elbows at the input and output ports were suspected. However, measurements at a frequency sufficiently away from resonance revealed that the reflection of the waveguide coupler alone was as good as S11 = 29 db. From this measurement, it was clear that the large return loss S11= 13 db appearing only at resonance was caused by the BOC cavity resonator. The resonance spectrum was checked for parasitic resonances close to the nominal resonance, both for the forward transmission ratio S21 with the output port 2 terminated by a matched load, and also for the reflection ratio S11 with a mobile short-circuit connected to the output port. For the S21-measurement of the traveling wave (TW) from port 1 to port 2, there was always one single resonance peak observed with a resonance width of about 280 KHz. However, for the reflection measurement S11 of the standing wave (SW) from the sliding short-circuit, two separate resonance peaks appeared with a variable frequency separation depending on the position of the sliding short-circuit. Due to the SW excitation of the cavity modes by a sliding short-circuit at the output port, the reflection measurement S11 has shown clearly that there are two SW resonant modes with slightly different frequencies f 1 and f 2 in the BOC cavity. By moving the virtual short-circuit plane from the odd numbered holes to the even numbered coupling holes, the two resonant frequencies f 1 and f 2 can be observed individually. If the BOC output is terminated by a matched load, the single resonance peak of the S21- measurement reveals that the coupling between the two modes is low and under-critical due to the orthogonal coupling of the λ g /4 multi-hole TW coupler. If the BOC output is terminated by a sliding short-circuit, the two resonance peaks indicate that the coupling between the two modes is stronger and over-critical because of the larger standing wave in the coupler, which excites two adjacent coupling holes with a phase difference of either 0 or 180 in time. However, a pure

5 4 traveling wave in the λ g /4 multi-hole waveguide coupler drives the two resonant modes of the cavity with a phase difference of 90 in space and in time and does not cause over-critical mode coupling, if the waveguide is terminated by a matched load and if the reflections from the WGbends and WG-load are negligibly small, S11= -29 db, as measured on the cold model. Amplitude and Phase Mismatch between the Two Orthogonal Modes of BOC As for any resonator with azimuthal multi-polarity, m=10 for BOC, the cavity has two orthogonal standing wave modes which are proportional to sin(mϕ) and to cos(mϕ), ϕ being the azimuth angle of the spherical coordinates in the equatorial plane. By definition, two exactly orthogonal modes do not couple to each other in a perfectly symmetrical cavity, but small geometric errors of the cavity can cause coupling between the modes of equal frequency, which eventually leads to power exchange and degenerate frequency detuning between mutually over-coupled modes. For two orthogonal SW modes in a cavity, the locus of maximum field strength of one mode coincides locally with zero field strength of the other mode. Therefore, in a λ g /4 multi-hole coupler, only every second coupling hole drives the same SW resonance mode in the cavity. Because there are 39 coupling holes of the BOC cavity, the first mode proportional to sin(mϕ) is driven by 20 coupling holes (n = 1,3,5 39), and the second mode proportional to cos(mϕ) is driven by only 19 coupling holes (n = 2,4,6 38). The resonant frequency of each mode is lowered by the coupling holes proportionally to their number. For equal frequency of the two orthogonal resonant modes of BOC, the number of coupling holes must be equal for both modes, i.e. the total number of odd and even coupling holes must be an even number. For this reason, a blind hole n = 40 has been drilled into the cavity wall behind the waveguide tee. From the transmission measurements S21 it has been found that the resonant frequency of the two modes in the cold model was reduced by about 700 KHz after 39 coupling holes had been drilled, corresponding to a frequency drop of approximately f = 36 KHz per hole of each mode. The half-power bandwidth BW of a loaded cavity at resonance is given by: BW = f 0 /Q L = f 0 (1+β 0 )/Q 0, where f 0 : resonant frequency, BW:3 db-bandwidth of loaded resonator, β 0 : coupling factor at f 0, Q 0 : quality factor of unloaded resonator, Q L : quality factor of loaded resonator, f: excitation frequency, δ: normalized frequency deviation, δ = 2Q 0 (f-f 0 )/f 0. The loaded Q L -factor of a cavity is measured by a network analyzer from the half-power bandwidth BW of the resonance. The coupling factor β 0 is obtained from the calibrated transmission factor Γ 0 = S21(f 0 ) of the pulse compressor by: β 0 = (1+ Γ 0 ) / (1- Γ 0 ). Through the coupling holes, the cavity fields radiate a wave E e emitted from the cavity into the waveguide. For a frequency difference f = f-f 0 between RF generator and cavity resonance and for steady state conditions, the emitted wave E e is proportional to the incident wave E k from the RF generator by 6 : 6 E.L.Ginzton, Microwave Measurements, McGraw Hill, New York, 1957.

6 5 E e = E k 2β 0 / (1+β 0 +jδ), for δ = 2Q 0 f /f 0, j = -1. The RF phase Φ between the incident and emitted wave of the cavity is a function of the normalized frequency deviation δ and the coupling factor β 0, and is expressed by: Φ = -atan(δ / (1+β 0 )) = -atan(2 f / BW), where f is the difference between the resonant frequency of the cavity and the frequency of the forced oscillation. If the resonant frequencies of the two quasi-orthogonal BOC modes are different by the amount f, there is also a phase difference Φ between the two waves emitted by the two cavity modes into the WG coupler, as given by the above equation for Φ. The two modes are no more orthogonal in the time domain, but they are still orthogonal in space because of the coupling holes. For the cold model BOC, a frequency difference f = 36 KHz causes a phase difference Φ = -14 for a resonance bandwidth BW = 287 KHz measured by the network analyzer. In Fig.7, the vector plot of the transmission factor Г(f) = S21(f) is shown, i.e. the ratio between the output and input field amplitude of BOC versus frequency f. The phase angle Φ 21 of the transmission factor S21 is given by: Φ 21 = atan(2β 0 δ / (β 0 2 -δ 2-1)). At the resonant frequency f 0, the RF phase of the incident traveling wave TW1 from the RF generator is perfectly synchronous with the two standing waves SW1 and SW2 in the BOC cavity, as the two standing wave modes are orthogonal in space and in time. According to the well known property of waves, a traveling wave can be represented by the superposition of two standing waves which are orthogonal in phase ωt and space kz: sin(ωt kz) = sin(ωt) cos(kz) - cos(ωt) sin(kz), where TW1 = sin(ωt kz), SW1 = sin(ωt) cos(kz), SW2 = -cos(ωt) sin(kz). The phase velocity of a traveling wave TW is given by v p = ω/k, with ω=2πf and k=2π/λ g. Two SW modes with unequal resonant frequencies f 1 < f 2 in the same BOC cavity, excited at the centre frequency f = (f 1 +f 2 )/2, oscillate with a phase difference of ±Φ/2. The two standing waves SW1 and SW2 of the cavity excite two traveling waves TW1 and TW2 propagating in opposite directions in the waveguide coupler of BOC: sin(ωt-φ/2) cos(kz) - cos(ωt+φ/2) sin(kz) = cos(φ/2) sin(ωt kz) - sin(φ/2) cos(ωt+kz). Compared to the ideal case Φ=0, the forward wave TW1 is smaller by a factor cos(φ/2), and the backward wave TW2 is proportional to sin(φ/2). The total power transported by the forwards and backwards re-emitted waves from the cavity into the waveguide coupler is constant, since cos 2 (Φ/2)+sin 2 (Φ/2)=1.

7 6 On the cold model BOC, the following RF parameters have been measured: β 0 = 10.4, Q 0 = For a difference f = 36 KHz between the two resonant frequencies, the normalized frequency deviation amounts to δ = 2.88, and the phase between the two SW modes is Φ = 14. For these parameters and for steady state excitation E k by the klystron, the normalized backward wave E r / E k of the cavity amounts to: E r / E k = α sin(φ/2) = db, for α = 2β 0 / ((1+β 0 ) 2 +δ 2 ) 0.5 = The theoretical value of the backward wave E r / E k and the measured reflection factor S11 of the cold model BOC agree rather well. For the next prototype cavity BOC1, the theory of a nonorthogonal phase between the two standing waves explained correctly why the measured reflection was even stronger: S11= -6dB, before a blind hole was drilled. The following RF characteristics have been measured on the prototype BOC1: Q 0 = before drilling the coupling holes, Q L = 26700, BW = f/q L = 112 KHz, β 0 = 6, f c = 600 KHz (frequency drop of cavity due to 39 coupling holes), f = 2f c /39 = 31 KHz (frequency drop of SW mode due to single coupling hole), δ = 2Q 0 f / f 0 = 3.86, α = 2β 0 / ((1+β 0 ) 2 +δ 2 ) 0.5 = 1.50, Φ = atan(2 f / BW) = 29. For these RF parameters, the normalized backward wave E r / E k amounts theoretically to: E r / E k = α sin(φ/2) = -8.5 db (without blind hole on BOC1). Despite the better mechanical precision, the reflection parameter S11 measured on the prototype BOC1 without blind hole was enormous, since the bandwidth of the loaded resonator, BW = f/q L = 112 KHz, was much smaller than for the cold model. Although it is possible to tune the two standing wave modes of BOC for equal resonant frequency by means of a blind hole in the cavity wall behind the coupler tee, there is still an asymmetry between the two orthogonal modes because of the unequal number of active coupling holes, which excite the sine mode in the cavity by 20 holes and the cosine mode by 19 holes. For equal size of all coupling holes, the field amplitude E 1 of the sine mode in the cavity is at first order a factor 20/19 higher than E 2 of the cosine mode. Even for an equal number of coupling holes for the two orthogonal modes, N 1 = N 2 = N/2, the TW coupler would induce a slightly weaker field of the downstream mode E 2 than for the upstream mode E 1. Because of the waves emitted from the cavity into the waveguide, the field strength in the waveguide drops stepwise by E at each coupling hole. Between the input and output port of the waveguide, the steady state field amplitude is attenuated by: E out / E in = Γ = (β-1)/(β+1), E in - E out = N E = 2 E in / (β+1). where β = β 0 / (1+jδ), From hole to hole, the TW field in the waveguide drops by: E / E in = 2 / N(β+1) = for N = 39, β 0 = 6.8, δ = 0.

8 7 The two orthogonal field modes in the BOC cavity are excited to different steady state amplitudes E 1 and E 2 by N 1 = 20 and N 2 = 19 coupling holes: E 2 / E 1 = (1- E/E in ) N 2 /N 1 = Each coupling hole emits half of the emitted field amplitude into the forward direction and the other half into the backward direction of the waveguide coupler. The waves emitted in the forward direction have all the same phase at the BOC output, where they add up for the steady state amplitude E f : E f = 20 E E 2 = E 1. Due to the regular interval λ g /4 between two coupling holes, the waves emitted by the two cavity modes in the backward direction cancel each other in the waveguide because of the alternating phase delay φ between even and odd numbered coupling holes: φ = (n-1)π at hole number n = 1,2 39. The backward emitted waves of the cavity add up with alternating signs ( 1) n-1 at the coupler input and build up the backward traveling wave E b : E b = 20 E 1-19 E 2 = 2.07 E 1. The ratio between the forward and backward waves is called the directivity d of the multi-hole coupler: d = E b / E f = , for f = 0. When the waveguide input port is driven by a RF signal that is switched on at time t = 0 to constant field amplitude V 1, and if the cavity was empty before, then the orthogonal fields F 1,2 (t) in the cavity rise towards the steady state values E 1,2 according to: F 1,2 (t) = E 1,2 (1-exp(-t/τ)), where τ = Q 0 / (1+β) π f 0 = 2.52µs for β = 6.8 Through the coupling holes, the cavity fields re-emit waves into the WG coupler proportionally to the emission factor α and the cavity fields F 1,2 (t). At resonance, the transient RF amplitude V 2 (t) at the coupler output port amounts to 3 : V 2 (t) = V 1 (-1+α(1-exp(-t/τ))), where α = 2β/(β+1) = 1.74 for β = 6.8 The reflected transient RF amplitude V 3 at the coupler input port is given by: V 3 (t) = V 1 αd (1-exp(-t/τ)), where αd = for β = 6.8 The unequal number of coupling holes causes an amplitude unbalance between the two orthogonal modes, resulting in a backward traveling wave and a steady state reflection loss S11= αd = -20 db at the input port of BOC.

9 8 The mismatch of the coupling factors of the two orthogonal modes amounts to β 1 /β 2 = (N 1 /N 2 ) 2 = 1.11, that can be checked by measuring the time constants τ of the exponential decay of the input and output signals S11 and S21 at the end of the RF pulse. The time constants of the free oscillations of the cold model measured for the input reflection and the output signal were different by 14%, because of the unequal coupling of the two orthogonal modes. When the BOC cavities will be used for RF pulse compression at CTF3, the transient regime of cavity loading will last for the time interval 0<t<T1. At the end of this interval at time T1=3.5 µs, the reflected amplitude at the input port amounts to V 3 (T1)= 0.07 V 1. Although this reflection is within the specification of the klystron, V 3 /V 1 < 0.22, care must be taken that the two orthogonal modes in the BOC cavity are tuned to the same resonant frequency. For klystron protection (S22< -13 db), the frequency mismatch f between the two BOC resonant modes must be rather small, since amplitude and phase unbalance between the two quasi-orthogonal modes cause cumulative reflection: f < f / Q L = 7 KHz. Small differences between the resonant and accelerating frequency, the coupling factors and the loaded quality factors of the two quasi-orthogonal modes cause reflection losses in the multihole coupler, resulting in a gain reduction and amplitude variation of the flat top of the compressed pulse. In order to know the effective RF parameters of the pulse compressor BOC, it is necessary to measure the quality factor Q 0, the coupling factor β, the time constant τ and the actual resonant frequency (f 1 +f 2 )/2 at the output port of BOC by means of a calibrated network analyzer. Already a small frequency difference between the two orthogonal cavity resonances and the accelerating frequency modifies substantially the transient amplitude and phase response at the pulse compressor output, see Fig.8. Simulation of RF Pulse Compression driven by Phase Modulation The phase modulation program for rectangular pulse compression has been calculated by solving the differential equation of the RF envelopes of the input voltage V 1 = A exp(jф 1 ) and the output voltage V 2 = B exp(jф 2 ) of the cavity resonators for constant output amplitude B during pulse compression 2 : V 2 + τ dv 2 /dt = Γ V 1 - τ dv 1 /dt. In the differential equation above, dv/dt signifies the time derivative of the vector voltages V, τ represents the time constant of the damped free oscillation, and Γ is the transmission factor Γ = V 2 / V 1 for steady state excitation without phase modulation. The phase modulation program at the compressor input is Ф 1 (t), and at the compressor output, the RF phase of the output voltage is Ф 2 (t). The power gain of the pulse compression is G = B 2 /A 2 = const. The two RF parameters τ and Γ completely define the dynamic response of the cavity resonators. By monitoring the transient response of the output signal versus time t during pulse operation, τ

10 9 and Γ can be measured very accurately directly at the pulse compressor output during the time intervals I and IV without fast phase modulation. There are three distinct time intervals with different phase programs, see Fig.10. I. 0 < t < 3.4 µs slow phase ramp for frequency shift KHz, II. 3.4 µs < t < 3.5 µs phase step Ф 0 with rise time Tr = 0.1 µs (0-100%), III. 3.5 µs < t < 5.0 µs phase modulation ФM during pulse compression, IV. 5.0 µs < t V 1 = 0, V 2 ~ exp(-t /τ): damped free oscillation at output. The slow phase ramp is superimposed to the compression phase program Ф 1 (t) during the entire pulse duration of the klystron, 0 < t < 5.0 µs, in order to introduce a frequency shift of about 140 KHz between the accelerator frequency and the resonant frequency of the pulse compressor. By this frequency shift of the pulse compressor, it is possible to reduce the phase variation of the compressed output pulse from about 80 to 8 during the pulse compression interval 3.5 µs < t < 5.0 µs. The phase program Ф(t) in Fig.10 is the superposition of the slow phase ramp with negative slope and of the phase function Ф 1 (t) for the pulse compression starting at time T1 = 3.4 µs with the fast phase step Ф 0. The simulation program of the pulse compression supposes that the klystron has a fast and accurate response to the phase modulation programmed by the low level RF electronics. The pulse compression by the LIPS cavities is started by a fast phase step Ф 0 = 68 with a short rise time Tr < 100 ns at the klystron output. The rise time of the phase modulation at the klystron output must be as short as possible for optimal power gain. In order to provide a fast phase response, the klystron must have a constant group velocity and constant amplitude gain over a large frequency bandwidth f >1/Tr = 10MHz. The resonant frequency of the five RF cavities of the klystron must be adjusted individually within this frequency bandwidth for a linear, nondispersive phase response versus frequency. At the factory, the klystrons have been tuned carefully for maximum output power and minimum rise time, which are obtained only for the nominal operating parameters of the klystrons. For the simulated pulse compression by a BOC in Fig.8, a phase step Ф 0 = 76 with a rise time Tr = 100 ns has been programmed at time T1 = 3.4 µs. The theoretical power gain is G = 2.05, and the phase sag is Ф 2 = 8.4 during the pulse compression of 1.5 µs duration. The phase modulation program spreads over a range 0 <Ф 1 <180, before the slow phase ramp is added. At the end of the pulse compression, the BOC cavity still contains 15% of the stored RF energy, what explains the low efficiency η = 0.61 of the pulse compression scheme for constant output power and low phase error. For CTF3, the last fraction of stored RF energy should not be used for pulse compression, because the non-linear phase error of the compressed pulse would drastically increase. Lowering the phase step at the beginning of the pulse compression to Ф 0 = 74 would reduce the theoretical compression gain to G =1.96 and the phase sag to Ф 2 = 7. Thereby the phase modulation program is restricted to 0 <Ф 1 <169. If the phase sag Ф 2 of the compressed pulse is too large for the CTF3 beam quality, the power gain must be reduced by programming a smaller phase step Ф 0 at the beginning of the pulse compression.

11 10 In reality, the theoretical power gain of the BOC pulse compressor is also reduced by the reflection loss and the insertion loss of the WG multi-hole coupler, which have been neglected in Fig.8. The insertion loss S21 of the WG coupler alone can be measured easily at a frequency sufficiently away from the cavity resonance. If the RF phase advance in the multi-hole waveguide coupler is not exactly 90.0 between coupling holes, the two standing wave modes in the cavity are not orthogonal and exchange RF power. Mode coupling happens frequently in overmoded high-q cavity resonators and is caused by small geometrical asymmetries of the cavity wall. Because of the unequal number of coupling holes of the sine and cosine mode of BOC, there is a standing wave inside the waveguide multihole coupler, which enhances the mode coupling. Ultimately, mode coupling in the overmoded cavity increases the power dissipation and reduces the time constant τ of the damped free oscillation. During the power tests of BOC1, the time constant τ measured in the time domain was considerably shorter than the theoretical value calculated from the RF parameters Q 0 and β, which had been measured by the network analyzer. It has been recognized, that it is more accurate to measure the time constant τ from the damped free oscillation at the compressor output, than to measure by the network analyzer the combined coupling factor β of two quasiorthogonal modes with unequal coupling factors, β 1 /β 2 = The coupling factor β of the pulse compressor is calculated from the measured values of the time constant τ and the unloaded quality factor Q 0 related by: τ = Q 0 / (1+β) π f 0 There may be some difficulties in calculating the accurate phase modulation program for BOC, if the resonant frequencies, the coupling factors and the time constants of the two orthogonal modes are different. Unequal modes lead to increased phase nonlinearity and amplitude sag of the flat top output of the pulse compressor. The effect of unequal coupling β 1 /β 2 = 1.10 between the two orthogonal modes of BOC is shown in Fig.8. Fortunately, any amplitude sag at the compressor output can be corrected by a self-learning algorithm in the feed-forward RF phase program for constant RF output power. Measured Pulse Response of High Power Klystron Amplifier and LIPS Cavities For maximum output power, the klystron is driven into saturation by a RF power input of about 200W. At the klystron output, the amplitude response is not linear at high power, and the klystron cannot be used for amplitude feedback control in the saturation regime. However, the phase response is perfectly linear even for maximum power output if the RF power input, the DC beam voltage and beam current of the klystron, and the currents of the focusing solenoids are set to the nominal values established at the factory for the maximum pulsed power MW of the klystrons.

12 11 The best of all klystrons tested during the year 2000 was an old, repaired tube TH2094 Ser.002R with more than hours of operation since The rise time for phase modulation steps of ± 90 was as short as t r < 35 ns 7. Due to the three amplifying cavities between the input and output cavity, the propagation delay through the klystron was as long as t pd =180 ns, see photo Φ4 of Fig.3. Because of the long propagation delay and the saturation of the klystron power, selfcorrecting feedback loops for fast amplitude stabilization of the klystrons were excluded. At the beginning of the pulse compression, the effect of the long propagation delay of a phase step through the klystron is visible on the klystron output power and on the LIPS output power. A slow dynamic response of the klystron to the fast phase modulation program can considerably reduce the theoretical power gain of the pulse compression 7. On photo Φ1 and Φ2 of Fig.3, the amplitude ripple of the klystron power output to the LIPS pulse compressor amounts to P/P = 6% ptp. This ripple is synchronous with the voltage ripple of the klystron supply voltage generated by the pulse forming network which causes both amplitude and phase ripple at the klystron output. On photo Φ4 of Fig.3, a phase ripple φ = 4 ptp has been measured at the klystron output, synchronous with the amplitude ripple oscillating with a frequency of about 1 MHz. The fast phase and amplitude oscillations of the klystron are enhanced by a factor 3x, if the klystron is loaded by the LIPS cavities with a narrow bandwidth BW = 170 KHz instead of a broadband water load. Fast phase modulation by PFN ripple is equivalent to frequency modulation of about 1 MHz, that causes a reactive impedance mismatch between the pulse compressor and the klystron, and hence a change of power gain. As the klystron ripple was very reproducible from pulse to pulse, the flat top of the compressed RF power pulse could be stabilized to better than P/P < ±1% by means of the fast and accurate feed-forward phase correction program, see photo Φ2 of Fig.3. The feed-forward phase modulation and the test arrangement with the high power klystron and LIPS pulse compressor are described in the CTF3-minutes 7, 8. The power gain of the LIPS pulse compression has been measured at the output of a klystron in December 2000: G =1.90 ± The measured gain was smaller than the theoretically expected value G =1.99 because of the insertion loss of the hybrid coupler of the LIPS assembly. The phase sag of the compressed output pulse was 8 ptp, as shown on photo Φ4 of Fig.3. During high power operation with the klystron, the time constant τ is the most important RFparameter that can be measured directly from the output waveform of the pulse compressor. The time constant τ is measured in two ways: either as the logarithmic decrement of the damped free oscillation after the end of the klystron pulse or from the zero crossing time t 0 of the cavity response, as shown by the waveforms PLI(t) in Fig.3 and P(t) in Fig.8. The zero crossing occurs at time t 0 during the time interval µs: 7 R.Bossart, LIPS pulse compression by phase modulation of klystron MDK35, Minutes of CTF3-meeting on , 8 R.Bossart, LIPS pulse compression by phase modulation of klystron MDK35, Minutes of CTF3-meeting on ,

13 12 t 0 = τ ln(2β/(β-1)) = τ ln(1+1/ Γ ). 9 It has been observed during several high power tests with different LIPS pulse compressors and klystrons, that the experimentally measured time constant τ was about 10% shorter than the theoretical value for a single cavity. Furthermore, the time constant τ measured from the zero crossing time t 0 of the forced oscillation was slightly shorter than for the exponential decay of the free oscillation after the end of the klystron pulse. These differences between time constants are due to imperfections of the hybrid coupler 3dB/90 which causes additional power losses. In order to compute the accurate transient response of the pulse compression, the time constant τ measured from the zero crossing time t 0 and the transmission factor Γ of the LIPS cavities without hybrid must be used for calculating the theoretical phase modulation program Φ 1 (t) of the pulse compressor. The measurement of the zero crossing time t 0 is easy and provides a direct indication of τ, as for large coupling factors β = 7...8, the logarithmic factor varies by 2.5% only. An accurate signal of the zero crossing time t 0 is provided by the phase measurement between the input and output of the pulse compressor, see Fig.8. At zero crossing time, t 0 = 2.0 µs for BOC with β = 7.2, the phase flips by 180º. If the phase flip is slow and not exactly 180º, the pulse compressor cavities are not correctly tuned for resonance. The linear term of the phase corrections of the feed-forward program during pulse compression shown in Fig.10 reveals that the resonant frequency of the LIPS cavities was not set exactly to the theoretical offset of 140 KHz from the accelerator frequency, as programmed by the feedforward phase control function. The linear term of the experimental phase corrections indicate that the average frequency of the two LIPS cavities was 13 KHz too high, since the phase corrections for optimum flatness during pulse compression necessitated an additional phase ramping of +6 during 1.3µs 8. With the theoretical phase modulation program at the klystron input, and without the feedforward phase corrections on during the pulse compression, the frequency error of the LIPS cavities caused two strong power overshoots of 13% each at the beginning and at the end of the pulse compression, see photo Φ1 of Fig.3. In fact, the reflected power at the LIPS input, shown on photo Φ3 of Fig.3, had been minimized by adjusting the resonant frequency of the two LIPS cavities by the mobile tuners. It is very useful to adjust the resonant frequencies of the two LIPS cavities, because the tuners can correct mismatches between a pair of orthogonal cavity resonators, especially during the pulse compression, when the total cavity reactance of the two resonators should be minimized. As the klystron is loaded by the narrowband LIPS cavities, the output power of the klystron does not stay stable and is growing during the pulse compression by nearly 10% within 1µs, see photo Φ2 of Fig.3. If the klystron is loaded by a broadband water load, the output power does stay constant in spite of the fast phase modulation. Hence, the dynamic response of the klystron depends strongly on the load reactance that changes rapidly with frequency for the high-q 9 R.Bossart, RF-Measurements and optimization of the coupling of the LIPS cavities for LIL, CERN/PS/LP Note 90-38(1990).

14 13 cavities of the RF pulse compressor. If the sign of the phase modulation is inverted, the output power of the klystron changes because of the different reactive impedance of the pulse compressor. The matching between the reactive input impedance of the pulse compressor and the klystron can be optimized by adjusting the electrical length of the waveguide connecting the pulse compressor to the klystron. Conclusions A BOC cavity with 38 equal coupling holes would have two orthogonal modes that are closely matched in resonant frequency and coupling factor. For a BOC cavity with 39 coupling holes, equal coupling between the two orthogonal modes is obtained if the diameters of the coupling holes of the cosine-mode are slightly larger than for the coupling holes of the sine-mode. The resonant frequency of the cosine-mode can be matched to the sine-mode by a blind hole with a fixed tuning screw. The mobile tuners of the LIPS cavities have a frequency resolution of 1KHz and provide a very useful fine tuning facility of the two orthogonal cavities. In order to minimize the residual phase error of a pair of pulse compressors, which may limit the beam quality of CTF3, the LIPS frequency can be fine adjusted during operation on every cavity for optimum matching of the reactive impedance during pulse compression. It has been demonstrated by the LIPS pulse compression tests with klystron MDK35 during the year ,8 that the feed-forward control method of the phase modulation program is easy to implement and that it is adequate for correcting both the amplitude and phase errors of the klystron and RF pulse compressor to the required accuracy for CTF3, namely P/P < 2% ptp and Φ = 8 ptp. The dynamic phase response of different klystrons will depend critically on the settings of the many klystron parameters. Theoretically, it is possible to compensate the systematic non-linear phase error Φ = 8 by two klystrons driven by a phase modulation program with opposite signs. However, since the dynamic response between two klystrons will be different for positive and negative phase modulation, an important residual phase error may persist. It is therefore of utmost importance, that the klystrons and pulse compressor cavities be tuned and matched for a similar dynamic phase and amplitude response, if the phase errors of the pulse compression shall not degrade the beam quality of CTF3.

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