High Bandwidth Wall Current Monitor

Transcription

1 High Bandwidth Wall Current Monitor A. D Elia, R. Fandos, L. Søby September 1, 2008 Abstract Wall Current Monitors (WCM) are commonly used to observe the time profile and spectra of a particle beam by detecting its image current. Within the framework of the EuroTeV Programme, a WCM for CLIC and ILC having a very large bandwidth (100kHz-20GHz) is required and has been developed. A deep study of the field configuration for the device has been necessary. Consequently, the geometrical parameters crucial for a proper functioning of the structure have been found. Three possible geometrical configurations were found. Two of them required a reduction of the geometrical aperture and were therefore rejected. The third one, which was chosen, has been fully characterized both from an electromagnetic and from a mechanical point of view. Furthermore, the very stringent initial requests (bandwidth from 100kHz to 20GHz) were reviewed in a more critical way showing that the low frequency cutoff can be sensibly increased. CERN, CH-1211 Geneva 23, Switzerland 1

2 Contents 1 Introduction 3 2 Field analysis The structure without feedthrough s: the gap resonances Feedthrough resonances Whole structure Summary of the field analysis Possible WCM structures First solution: reduction of the beam pipe aperture Single device structure Double device structure Second solution: introducing an intermediate coaxial without changing the aperture Summary of the solutions Mechanical design and assembling SiC design and characterization and the final whole structure Longitudinal coupling impedance evaluation 22 6 Low frequency cutoff: do we really need 100 khz? How to properly recover the signal WCM bunch train recovering CLIC Beams ILC Beams An academic example The testbench 33 8 Conclusions 34 2

3 1 Introduction The stringent requests of ILC and especially CLIC beams translate into tight requirements of beam diagnostics device performances. In fact, because of the quite short bunch spacing in CLIC, the WCM needs a very high frequency cutoff of 20GHz, with, in principle, a very large bandwidth from 100kHz to 20GHz. Allowing for these high frequencies, a deep study of the field configurations for the device is necessary in order to pin down the geometrical parameters crucial for a proper functioning of the structure. Three possible geometrical configurations were found: two of them required a reduction of the geometrical aperture and were therefore rejected; the third one, which was chosen, has been fully characterized both from an electromagnetic and from a mechanical point of view. Furthermore, the very stringent initial requests (bandwidth from 100kHz to 20GHz) were reviewed in a more critical way. It turned out that such a low frequency cutoff is not realistic. The value of 100kHz was chosen because of the very long bunch train length in the Drive Beam Linac of the 3rd CLIC Test Facility (CTF3) at CERN (1.54µs, namely 700kHz in frequency) [1]. A first effect of the low frequency cutoff is to give an exponential droop of the signal with a time constant τ L = 1/3f low, where f low is the low frequency cutoff. This effect could be dangerous if the droop time constant τ L is comparable or lower than the bunch length in time; but this is not the case because of the very short expected r.m.s. bunch length for CTF3 of 5ps 1. Finally the only remaining macroscopic effect is that the mean level of the bunch train signal will go to zero with the same exponential law and can be compensated in many cases by external circuits or by post processing. A more serious problem is the possible influence of the low frequency cutoff in relation to the signal recovering. In our case, in which we want to solve not the single bunch shape but only the bunch train shape, a correct signal recovering will happen if one is able to detect the first harmonic peak or two adjacent peaks in the spectrum. If a certain number of bunches are lost the new spectrum will present the first harmonic at a lower frequency and a shorter frequency separation between the harmonic peaks (larger bunch separation in time). Therefore for a proper recovering of the signal one should be able to detect this new first harmonic at a lower frequency or two adjacent harmonics at higher frequencies, meaning that the merit figure for the signal recovering is the bandwidth which should be able to follow this frequency shift. The minimum required bandwidth is fixed as one half of the highest frequency that we want to detect. Our worst case is for CLIC Drive Beams having a bunch spacing of 83ps meaning that the first harmonic is at about 12GHz 2 giving a minimum required bandwidth of 6GHz. The expected low frequency cutoff of the proposed device is 2GHz (with the possibility of lowering it down to 400MHz by means of an external circuit) while the high frequency cutoff is 20GHz for a bandwidth of 18GHz which is three times what we need and with the further simplification of avoiding any ferrite. 1 The ILC and CLIC final values are even lower of 1ps and 3.33ps, respectively. 2 The bunch spacing for CLIC Main Beam is 500ps ( 2GHz) while for ILC beams it is 369ns ( 3MHz). 3

4 2 Field analysis The working principle of the proposed structure is shown in figure 1: the electromagnetic field dragged by the bunches passes in a small longitudinal gap made on the wall pipe and it is shaved. A part of this portion of the electromagnetic field is captured by a coaxial antenna in the first section of a bigger coaxial line, while the rest is damped along the line. Figure 1: Principle scheme of a Wall Current Monitor: the field dragged by a particle bunch is shaved by the outer pipe and captured by the feedthrough s. Since the cross sections of the outer and inner pipe are different not all the possible field configurations may propagate from the inner to the outer structure. Furthermore the presence of the feedthrough s gives a further source of resonances related to the distance from a feedthrough to the adjacent one. In the following we shall analyze the different reflection sources of the structure by considering each one separately and finally putting everything all together, as done in [2]. 2.1 The structure without feedthrough s: the gap resonances It is known that the fields of a particle moving at the speed of the light along the axis of an infinite waveguide exhibit a TEM modal structure [3]; therefore a very thin wire stretched along the axis of our Device Under Test (DUT) allows to simulate the passage of a particle beam. Figure 2 shown the structure 3 we are analyzing by means of CST Microwave [4]. The outer pipe has a smaller section with respect to the inner pipe; this means that some of the allowed propagating modes of this last one cannot propagate by the outer pipe as shown in figure 3. We call them gap resonances. Furthermore, due to the considerable capacity across the gap, this structure presents a rather fast decreasing of the signal with frequency. By smoothing the transition by means of a tapering, one reduces the gap capacity effect and the signal gets better as shown in figure 4 [2]. 3 Note that the inner coaxial radius is fixed by the design dimension of CTF3 beam pipe. 4

5 Figure 2: Analyzed structure with its geometrical parameters: the structure is fed by a TEM mode from the Port1; note the different cross section values of the inner and outer pipes of 19.5mm and 4mm, respectively, giving two different values of the TM01 cutoff of 6.9GHz and 35GHz, respectively S31(dB) TM TM Frequency (GHz) Figure 3: Transmission of the signal at the port 3 (outer pipe): the first gap resonance appears at 6.9GHz and the second at 14.8GHz. Figure 4: Tapered structure on the left hand side (50mm tapering length); scattering parameters on the right hand side: the structure is fed by a TEM mode from the Port1, S11 is the reflection of the signal at the Port 1 while S21 and S31 are the transmissions of the signal at the Port 2 and 3 respectively. 5

6 2.2 Feedthrough resonances When the distance between two feedthrough s becomes equal to the free space wavelength, the first azimuthal resonance appears in the structure with the following rule: F feed = c, with d feed = 2π r d feed n where c is the speed of light, n is the number of feedthrough s and r is the height of the feedthrough evaluated at half size of the distance between the inner and outer pipes, as in figure 5 where an example for a structure having four feedthrough s is shown [2]. (1) Figure 5: Example of feedthrough resonances; in this case with a number of feedthrough s n=4. It is straightforward that by increasing the number of feedthrough s, the first feedthrough resonance will be pushed to higher frequencies. By choosing n=16, with the same r, this resonance is pushed up to 33GHz. 2.3 Whole structure When putting all together 4, the WCM response shows a similar behavior to figure 4 but presenting an enhancement of the gap resonances, as shown in figure 6 [2], where a slice of 1/32 th of the structure has been simulated by HFSS [5]. This happens since the presence of feedthrough s gives a further limitation in space for the gap resonances which starts to resonate also in the azimuthal direction and which, globally, enhances the reflected signal (see figure 7). In figure 8, it is shown a study of this effect for the first TM01 gap resonance for a different number of feedthrough s. The best condition, giving the same signal as in figure 4, will be achieved for a distance between two adjacent feedthrough s at least equal to the TM01 gap resonance wavelength d feed = 2π n r λ TM01. (2) 4 The geometrical parameters of the simulations stays the same as used in the previous sections if not otherwise specified. 6

7 Figure 6: Simulated structure with its scattering parameters: the structure is fed by a TEM mode from the Port1, S11 is the reflection of the signal at the Port 1, while S21, S31 and S41 are the transmissions of the signal at the Port 2, 3 and 4 respectively. Figure 7: The wave traveling towards the feedthrough s should present a wavelength λ d v,feed in order to freely pass through feedthrough 12 feedthrough 16 feedthrough 16 S41 (db) Frequency (GHz) Figure 8: First gap resonance for a different number of feedthrough s. 7

8 2.4 Summary of the field analysis The structure field analysis gives two requirements concerning the feedthrough resonances and the effect of the feedthrough enhancement on the gap resonances in conflict one to each other: Feedthrough resonance F feed = c 2π ( r/n) = c d feed Gap resonance d feed = 2π n r λ TM01 d feed has to be, on one hand, as small as possible and, on the other hand, at least equal to the TM01 wavelength. A trivial solution of the problem should be to push the frequency of the TM01 mode beyond 20GHz by scaling the dimensions of the whole structure. The scaling factor is rather low, 0.37, showing a huge reduction of the beam pipe aperture from 20mm to 7.4mm which is obviously not acceptable. 3 Possible WCM structures It is possible to overcome the impasse on the d feed value found in the previous section in two ways: 1. by reducing the outer pipe aperture to a reasonable quantity, in order to permit the gap resonances excited at its edge to run back in the beam pipe; 2. by playing with the field configurations of a double coaxial waveguide, in order to avoid the gap resonances enhancement. Since the requirements on the low frequency cutoff are in principle 5 quite stringent (100kHz), we developed two versions for the first item: a single device structure with a higher low frequency cutoff; a two device structure by splitting high and low frequency response, in order to decrease as much as possible the low frequency cutoff. 3.1 First solution: reduction of the beam pipe aperture The leading idea of this solution is to permit the trapped modes excited at the edge of the outer pipe to run back in the beam pipe as shown in figure 9 in which a comparison for different structures without feedthrough s and with and without aperture reduction is presented. This permits to have smaller gap resonances as shown in figure 10 in which a comparison for a structure with and without feedthrough s is analyzed, and permits of finding a compromise for d feed for the condition in subsection The question of the low frequency cutoff value will be fully undertaken in section 6. 8

9 Figure 9: Comparison between a structure with a 2mm aperture reduction (1) and two structures without reduction, tapered (2) and non tapered (3). Figure 10: Comparison between a structure with a 2mm aperture reduction with and without feedthrough s; in this case the number of feedthrough s is 8. 9

10 3.1.1 Single device structure A compromise for the condition in section 2.4 has been found in a d feed =12.37mm (first F feed 24GHz) as in the structure shown in figure 11. The tapering cone, accompanying the aperture transition, is added for mechanical continuity and smooths the radiation propagation in the structure. Figure 11: Structure with its geometrical parameters. The structure presents very attractive mechanical behaviors: it presents only 8 feedthrough s 6 and it is very compact (whole length less than 50cm) and easy to machine. Unfortunately the beam pipe radius passes from 20mm to 16.5mm in order to have d feed =12.37mm with 8 feedthrough s; in any case the transfer function shown in figure 12 is rather interesting. Figure 12: Transmission at the feedthrough for a structure without SiC. 6 Larger the number of the feedthrough s more difficult will be the assembling of the structure. 10

11 In the real device the waveguide ports must be replaced by an absorbing material. The radiation going to port 3 can be absorbed by using a layer of silicon carbide (SiC). The result can be seen in figure 13, using a SiC piece of dielectric permittivity ǫ r =30 and dielectric loss tangent tanδ =0.3, both constant in the whole frequency range. Figure 13: Transmission at the feedthrough for a structure with SiC. The presence of the SiC gives a quite high low frequency cutoff at 6.2GHz, even if it is possible to compensate by external circuits the first part of the signal in order to reach a lower low frequency cutoff. The characteristics of this structure can be summarized as in the table below. Pro Cons 1. Only 8 feedthrough s 1. Beam aperture reduced by a factor of 1/4 2. Very easy mechanical design and 2. High low frequency cutoff with SiC quite short structure ( 50cm) Double device structure The leading idea of this structure is to split the device in two parts, one with a good response at high frequencies and the other one having a good response at low frequencies. The high frequency part working principle is as treated in the previous section; the low frequency part is a simple tapered WCM supporting 4 feedthrough s with the possibility of allocating a huge volume of ferrite in the back of the structure in order to lower as much as possible the low frequency cutoff. The fundamental constraint of this structure is that the two signals have to be postprocessed before a new bunch train comes in. In the worst case (in the final part of the Drive Beam Accelerator), the bunch trains are separated by 70ns ( 14.3MHz)[6], allowing for signal acquisition frequencies of about 30MHz which are quite affordable. However this solution would also need some sophisticated electronics before the oscilloscope. 11

12 Figure 14 shows a structure in which a first part, on the left side, is devoted to the high frequency response, the second part, on the right side, is for the low frequency response. Figure 14: Geometrical parameters and 3D representation of the structure used for the simulations in HFSS; the high frequency part presents 12 feedthrough s while only 4 for the low frequency part. It is possible to study the two parts separately giving the following results (figure 15 and 16). Figure 15: Transmission at the feedthrough s for the high frequency part. The high frequency structure gives a low frequency cutoff at 5.5GHz, while the low frequency structure has a high frequency cutoff of 5.2GHz: for a frequency range of about 300MHz the two signals do not overlap. Furthermore the high frequency part foresees an aperture reduction from 20mm to 17.5mm in order to keep the gap resonances in the range ±1.5dB. 12

13 Figure 16: Transmission at the feedthrough s for the low frequency part. Figure 17: Transmission at the feedthrough s for the whole structure. The whole structure gives the result as shown in figure 17. It has to be noted that the two structures, when together, talk to each other (note that now the gap resonances are in the range ±2dB); by playing with the geometrical parameters (for example with the tapering) it is possible to improve the signal. Figure 17 still shows 300MHz of non signal overlapping; it is possible to compensate it either by external circuits or by postprocessing one of the two signals in this range. Finally the structure can be summarized as follows: Pro Cons 1. Possibility of fully covering the 1. Need some not easy electronics 100kHz-20GHz bandwidth before the oscilloscope 2. Reasonable number of feedthrough s 2. Long structure ( 70cm) (12 for the high frequency part and 3. Aperture reduction for the high only 4 for the low frequency part) frequency part 13

14 3.2 Second solution: introducing an intermediate coaxial without changing the aperture The leading idea of this third structure is to preserve the beam pipe aperture of 20mm radius, by playing with the field configurations of a double coaxial waveguide. The diameter of the pipe to which the feedthrough s are connected (outer pipe in figure 18) is increased and a second pipe (inner pipe in figure 18) is added for two fundamental reasons: mechanical continuity of the beam pipe and shielding of the feedthrough s from the reflections of the TM gap resonances. This effect is schematically shown in figure 18, where it is shown how the TM01 mode coming from the beam pipe is reflected back 7 at the surface A without arriving to the feedthrough s: this produces the same behavior of a structure without feedthrough s as shown above in figure 4. Figure 18: Working principle of the structure: the TM01 mode of the beam pipe (cutoff frequency 6.9GHz) does not enter in the inner pipe and will be reflected back (red arrow) at the surface A, never reaching the feedthrough s that are shielded; the cutoff of TM01 mode of the inner pipe is out of our range of interest (32GHz). In figure 19 and 20 are shown the scattering parameters for two structures with or without the inner coaxial. 7 The same for TM02 mode. 14

15 Figure 19: Above, proposed structure with its geometrical parameters; below, scattering parameters: note that the transmitted signal is very similar to the signal in figure 4. 15

16 Figure 20: Above, simulated structure without inner coaxial; parameters. below, scattering 16

17 In order to absorb the e-m radiation going into the inner and outer pipes we put a layer of SiC and we readapt the cone length as shown in figure 21. Figure 21: Above, positioning and shaping of the SiC (in brown); below, transmission at the feedthrough. The behavior of the third structure can be summarized as in the table below. Pro Cons 1. Very good signal staying in a 1. Large number of feedthrough s (16) ±1.5dB range from 2GHz to 20GHz 2. Not easy in terms of mechanics 2. No aperture reduction and assembling 17

18 3.3 Summary of the solutions A summary of the three structures is presented in figure 22: since in our case any aperture reduction is not acceptable the third structure has been chosen as the first two structures present an aperture reduction of 30% and 15%, respectively. Figure 22: Summary of the proposed structures, in the red box the chosen structure is shown. 4 Mechanical design and assembling One of the requirements for the WCM is to have dismountable feedthrough s in order to allow their replacement if they break. This requirement makes the design more complicated. In figure 23 the feedthrough welded into an ad hoc dismountable flange is shown. In figure 24 it is possible to see the solution found for inserting the pins into the outer pipe. The pipe to which the feedthrough s are connected, made in copper, presents some slots: by using a special developed tool it is possible to open these cuts and to insert the feedthrough pins; when the tool is removed, the pins will be held in place due to the elasticity of copper. It is possible that this procedure will give some error in the feedthrough positioning, in particular the pin may be tilted with respect to the ideal central axis. It is very important to evaluate this tilt: this may give an error in the feedthrough line impedance (50Ω in the coaxial part). In the worst case, it gives a maximum displacement of ±0.2mm, meaning a new line impedance of 33Ω. In a more realistic case, the displacement value should 18

19 be about one half of the previous value, giving a line impedance of 46Ω. In figure 25 it is possible to see the maximum misalignment error between the two conductors and the change of the line impedance for different values of this misalignment: at 46Ω the reflection of the signal in the feedthrough coaxial line is only -27dB (in the worst case of 33Ω it is -14dB). Figure 23: Feedthrough welded into a flange ad hoc designed in order to have 16 feedtrhough s all around. Figure 24: On the left hand side: tool for inserting the feedthrough s; On the right hand side: positioned feedthrough s. 19

20 Figure 25: On the left hand side: evaluation of the maximum misalignment error between inner and outer conductors; On the right hand side: Change of the line impedance versus displacement: in the red circle is outlined the realistic achievable displacement error giving a quite low signal reflection ( -27dB); in the reflection coefficient formula is Z 0 =50Ω corresponding to an ideal alignment, while Z L is the impedance value for a displacement of 0.1mm SiC design and characterization and the final whole structure The SiC is another intricate point of the project. It has to absorb the whole electromagnetic radiation going into the two coaxial lines in a very wide bandwidth (2GHz-20GHz) in order to avoid reflection at the shorted ends. The efficiency of this absorption will determine in practice the characteristics of the WCM. In order to estimate the electrical permittivity of the SiC, a simple setting with a piece of SiC into a waveguide that fits the frequency range of interest has been designed and built. The transmission coefficient S21 has been measured with a Network Analyzer. The value of S21 is affected by the value of the electric permittivity of the SiC piece inside the waveguide. The same geometry is simulated in HFSS, for different values of the electrical permittivity and loss tangent δ. The electrical permittivity and loss tangent δ that are chosen for each frequency are the ones minimizing the difference between the corresponding S21 produced by HFSS for that values and the S21 parameter measured with the Network Analyzer. The result of the characterization is as follows freq (GHz) ǫ r tan δ The SiC geometry for the internal coaxial is quite simple, see figure 26, while the geometry for the outer coaxial is rather complicated since the space between the two tubes is only 1mm and quite long cuts are needed in order to efficiently absorb the signal (figure 27). 20

21 Figure 26: Design of the internal piece of SiC. Figure 27: Design of the outer piece of SiC. 21

22 The whole structure is shown in figure 28. In figure 29 it is shown a simulation in HFSS taking into account the final real geometry (i.e. outgassing tubes, the cut in the external pipe for inserting the feedthrough...) and the real behavior of the SiC. The response is within ±2dB in the range 2GHz-20GHz. Figure 28: Cut view of the final design. Figure 29: Transmission at the feedthrough for the real structure with the real SiC behavior. 5 Longitudinal coupling impedance evaluation The longitudinal impedance can be measured by scattering parameters. For reciprocal and symmetric circuits, in the case of matched lines (characteristic impedance equal to the reference impedance, as in the case of our HFSS simulations), the only nonzero scattering parameter is: S 12 = e jkl, (3) 22

23 where the propagation constant k can be written in terms of the distributed parameters of the line. By defining a propagation constant of a reference pipe, k r, and another propagation constant of the device under test (DUT), k d, it is possible to get the longitudinal impedance as, (kd 2 Z // = jz k2 r )l2 0, (4) k r l where Z 0 is the reference characteristic line impedance. In terms of scattering parameters by using the well-known improved log-formula [7] we get, Z // = Z 0 log S 12 r ( S 1 + log S d ) 12, (5) 12 d log S12 r where S r,d 12 is, respectively, the scattering parameter of the reference pipe or of the DUT. In particular in case of lossless lines it is, S r 12 = e jφr, (6) with Φ r = ωl c, while for DUT it is S d 12 = S d 12 e jφ d, (7) which gives as real and imaginary parts of the impedance [8] R(Z // ) = 2Z 0 log S d 12 ( 1 + Φ Φ r ) (, I(Z // ) = 2Z 0 Φ 1 + Φ 2Φ r ) + Z 0 log 2 S d 12 Φ r, (8) with Φ = Φ d Φ r. The results, see figure 30, show low impedance values meaning that the device does not give any inconvenience to the beam passing trough. Re Z // (Ω) Frequency (GHz) Im Z // (Ω) Frequency (GHz) Figure 30: Real and Imaginary parts of the longitudinal coupling impedance. 23

24 6 Low frequency cutoff: do we really need 100 khz? The request of 100kHz low frequency cutoff comes from the very long bunch pulse of 1.54µs (namely 700kHz) of CTF3 drive beam Linac. A first effect of a higher low frequency cutoff is to give an exponential droop of the signal with a time constant τ L = 1/3f low, where f low is the low frequency cutoff. This effect could be dangerous if the droop constant time τ L is comparable or lower than the bunch length in time: in this case the single bunch signal will be distorted. The r.m.s. expected bunch lengths of 1ps and 3.33ps for ILC [9] and CLIC [10], respectively, give a rather large safety threshold. Thus leaving only the macroscopic effect that the mean level of the bunch train signal will go to zero. A more serious problem is the possible influence of the low frequency cutoff for a proper signal recovering. A correct signal recovering 8 will happen if one is able to detect the first harmonic peak or two adjacent peaks in the spectrum. If a certain number of bunches are periodically lost 9 the new spectrum will present the first harmonic at a lower frequency and a shorter frequency separation between the harmonic peaks (larger bunch separation in time). Therefore for a proper recovering of the signal one should be able to detect this new first harmonic at a lower frequency or two adjacent harmonics at higher frequencies, meaning that the merit figure for the signal recovering is the bandwidth which should be able to follow this frequency shift. The minimum required bandwidth is fixed as one half of the highest frequency that we want to detect. In our case the minimum required bandwidth is of 6GHz determined by CLIC Drive Beam with its 83ps of bunch spacing (12GHz) representing the worst condition since the bunch spacing for the CLIC Main Beam is 500ps ( 2GHz) while for ILC beams it is 369.2ns ( 3MHz). The expected high frequency cutoff of the proposed WCM is 20GHz while the expected low frequency cutoff is 2GHz (with the possibility of lowering it down to 400MHz by means of external circuits) which gives a very large bandwidth of 18GHz able to fully accomplish the signal recovering. In the following, by using an ad hoc code in Matlab, we shall give some numerical examples of these effects and, finally, we shall apply the real WCM transfer function to different typology of bunch trains, showing that the signal is always fully recovered. 6.1 How to properly recover the signal In figure 31 it is shown a bunch train having the following behavior: 8 In principle, a proper recovering of a signal will happen only by filtering the signal from DC till the maximum frequency characterizing its spectral shape, in our case determined by the inverse of two times the r.m.s. bunch length: in the case of CLIC Drive Beam (representing the worst case), it is 2σ=6.66ps corresponding to 150GHz! For our purpose it is not needed to solve the single bunch shape, but only the bunch spacing (83ps corresponding to 12GHz). 9 Note that non periodical bunch missing will give only a phase shift in the spectrum without any consequence in the signal recovering. 24

25 Bunch separation 83ps RMS bunch length 3.33ps Train duration 8.3ns Nb of bunches 100 Peak current 293A Figure 31: Gaussian bunch train. We apply to this signal a perfect low pass filter starting from DC and having the original required specifications of a high frequency cutoff f high =20GHz as shown in figure 32. The result is shown in figure

26 Figure 32: Spectrum of a Gaussian bunch train to which we apply a perfect low pass filter. Figure 33: Time signal recovering: it is possible to appreciate exactly the bunch spacing of the input signal (83ps). 26

27 In figure 34 it is shown the recovering signals in time of the same previous bunch train by applying three different filters: the first one is able to detect only the first harmonic at 12GHz (red line); the second one is able to detect only the second harmonic at 24GHz (black line); the last one is able to detect the second and third adjacent harmonics at 24GHz and 36GHz (magenta line). The result is that only the signal recovering in time coming from the first and third filters is correct, while the application of the second filter gives a bunch spacing of one half with respect to the real one; as already mentioned, to properly recover the signal, we need to detect the first harmonic or two adjacent harmonics. Figure 34: Three different filters are applied to the bunch spectrum: the first one is centered at 12GHz with a bandwidth of 4GHz (red line), the second one is centered at 24GHz with still a bandwidth of 4GHz (black line) and the third one is centered at 30GHz with a bandwidth of 14GHz (magenta line); the second filter able to detect the second harmonic in the spectrum gives a wrong signal recovering (bunch spacing of 42ps); note that the ripple in the third recovered signal is due to the superposition of the two detected harmonics in the Fourier analysis. Now we consider a new bunch train having the same behavior as the previous train but after every bunch there is one missing, figure 35. In figure 36 it is shown the spectrum of this new bunch train which differs by the previous one by having the harmonic at 6GHz and 6GHz spacing instead of 12GHz 27

28 Figure 35: Gaussian bunch train with 50 bunches. (larger bunch spacing in time). In order to correctly recover the time signal it is sufficient to apply a filter centered at 9GHz and with a bandwidth 6GHz. Figure 36: On the left hand side: spectrum of a 50 bunch train to which we apply a filter centered at 9GHz and with a bandwidth of 8GHz (magenta line), in the red circle the new harmonics due to the larger bunch spacing are highlighted; on the right hand side: the signal recovering after the filtering. This states the worst condition of our input signal. In fact if more bunches are periodically lost, the spacing between two adjacent harmonics proportionally reduces: if after every bunch there are two lost, the spacing will be of 4GHz, if three, the spacing will be 3GHz and so on. Therefore the minimum required bandwidth will be fixed by one half of the highest frequency that we want to detect which is fixed, in our case, with the 12GHz of the CLIC Drive Beam giving a minimum required bandwidth of 6GHz. 6.2 WCM bunch train recovering The proposed WCM with its 18GHz of bandwidth gives a quite safe margin for a correct signal recovering without any ferrite required. In the following the application of the WCM real signal to simulated CLIC-like and ILC-like beams will be done; finally it will be showed an academic example with a very noisy signal. 28

29 6.2.1 CLIC Beams The signal showed in figure 31 presents the typical 10 behavior of a bunch train flowing in the CLIC Drive Beam Accelerator: the distance between two adjacent bunches is of 83ps, the r.m.s. bunch length is 3.33ps. We apply the output of the HFSS simulation to this signal and the result can be seen in figure 37. Figure 37: Application of the WCM as a filter to the bunch train: on the top it is shown the WCM behavior and its application to the bunch train spectrum; below the signal recovering in time. 10 The real CLIC Drive Beam bunch train will present 2904 bunches, in our simulation we have been using only 100 bunches for calculation reasons without any relevant changing in the physical meaning of the treated subject. 29

30 The signal showed in figure 38 represents the typical 11 bunch train of CLIC Main Beam: the bunch separation is of 0.5ns and the bunch length in damping ring before extraction is of 5.1ps. Figure 38: Example of a CLIC Main Beam bunch train. The application of the WCM signal to the spectrum and its time recovering is shown in figure 39. Figure 39: Above: frequency spectrum of the CLIC Main Beam bunch train (blue line) with WCM signal windowing (magenta line); below: time signal recovering. In both cases our filter is able to fully recover the correct signal. 11 The real CLIC Main Beam bunch train will present 312 bunches, see previous note. 30

31 6.2.2 ILC Beams A typical 12 ILC bunch train presents a r.m.s. bunch length of 1ps and a bunch spacing of 369.2ns as shown in figure 40. Figure 40: Example of ILC two bunch train. The signal recovering in time is in figure 41. Figure 41: Time signal recovering after WCM application. Also for ILC beams our WCM is able to fully recover the bunch train signal An academic example As a final academic example we analyze by using the WCM a signal having a random noise level of about 10% with respect to the signal amplitude and also a certain number of bunches missing. The beam signal is shown in figure 42 and its recovering in figure The real ILC bunch train will present 2625 bunches, see previous note. 31

32 Figure 42: Beam signal. Figure 43: The WCM signal recovering in time. 32

33 Also in this very problematic case the signal is pretty good recovered. It is important to stress that no ferrite is required for the structure. 7 The testbench The experimental setup foreseen for characterizing the WCM can be schematically seen in figure 44: we are dealing with a coaxial line having a 50Ω line impedance with the Device Under Test (DUT) situated in the middle. Figure 44: Sketch of the experimental setup. Because of the beam pipe diameter of 40mm, the internal wire of the testbench is to be 17.4mm of diameter for a 50Ω impedance. The dimensions of the connectors at the end of the line are 2.9mm external diameter and 1.26mm internal diameter. A cone of a length of 15cm slowly smooths the transition between the straight tube of the testbench and the connectors, as shown in figure 45. Two pieces of teflon, at both sides at the end of the adaptive cones, give the mechanical stability to the inner wire. Figure 45: Design of the cone of the testbench with a zoom of the final connector piece. The simulation results of the testbench are presented in figure

34 0 10 S11 S21 20 S parameters (db) Freq (GHz) Figure 46: Signal transmission (S21) and reflection (S11) of the testbench. 8 Conclusions The development of a 20GHz Wide Band Current Monitor has reached its final phase. The electromagnetic fundamental relations for this kind of devices have been found giving three possible structures as good candidates; since two of them presented a reduction of the aperture, they have been rejected. The chosen structure presents a quite flat behavior of the signal transmission at the feedthrough s staying in a range of ±2dB around 24dB, in a frequency range from 2GHz to 20GHz. The mechanical design is finished and all the parts for one prototype have been ordered. Furthermore the initial very stringent specifications on the low frequency cutoff (100kHz) have been reviewed in a more critical way. For very short bunches as in ILC and CLIC (1ps and 3.33ps, respectively), the only effect of the low frequency cutoff is to give an exponential droop to the mean value of the whole bunch train signal; this effect can be compensated (only for CLIC) in many cases by external circuits or by post processing. A more serious problem is the possible influence of the low frequency cutoff for a proper signal recovering. A correct signal recovering will happen if one is able to detect the first harmonic peak or two adjacent peaks in the spectrum. If a certain number of bunches are periodically lost the new spectrum will present the first harmonic at a lower frequency and a shorter frequency separation between the harmonic peaks (larger 34

35 bunch separation in time). Therefore for a proper recovering of the signal one should be able to detect this new first harmonic at a lower frequency or two adjacent harmonics at higher frequencies, meaning that the merit figure for the signal recovering is the bandwidth which should be able to follow this frequency shift. The minimum required bandwidth is fixed by one half of the highest frequency that we want to detect. In our case the minimum required bandwidth is of 6GHz determined by CLIC Drive Beam with its 83ps of bunch spacing (12GHz) representing the worst condition since the bunch spacing for the CLIC Main Beam is 500ps ( 2GHz) while for ILC beams it is 369.2ns ( 3MHz). The expected high frequency cutoff of the proposed WCM is 20GHz while the expected low frequency cutoff is 2GHz (with the possibility of lowering it down to 400MHz by means of external circuits) which gives a very large bandwidth of 18GHz able to fully accomplish the signal recovering with the further simplification of avoiding any ferrite in the structure. Finally the new improved testbench has been presented, showing a flat transmission response with quite low reflections (<-10dB). The first bench tests on the prototype followed by beam test are foreseen in the end of the year. Acknowledgements This work is supported by the Commission of the European Communities under the 6 th Framework Programme Structuring the European Research Area, contract number RIDS We would like to thank Tom Kroyer for the fundamental work done in the past on this subject and for his fundamental suggestions and comments on the several topics treated in this report. Thanks to Ivan Podadera for the important support during his stay at CERN. Many thanks to the mechanical designers Pierre Bourqin and Vincent Maire able to find proper and innovative solutions to the very difficult mechanical challenges. Thanks to Claude Achard who took charge of the SiC. Thanks also to Giovanni Rumolo who gave us many clarifications about beam particle spectra that have been crucial to pin down the fundamental parameters of the structure. Thanks to Vittorio G. Vaccaro for fruitful discussions. Many thanks to the CERN CLIC Group which supported this work with very important suggestions and comments. References [1] CTF3 parameters at parameters.htm. [2] T. Kroyer, A Structure for a Wide Band Wall Current Monitor, EUROTEV- REPORT and AB-Note RF. [3] D. Davino, M. R. Masullo, V. G. Vaccaro, L. Verolino Coaxial Wire Technique: A Comparison Between Theory And Experiment, INFN-TC

36 [4] Computer Simulation Technology at [5] Ansoft Corporation at [6] H. Braun et al., Updated CLIC Parameters 2005, CERN-OPEN ; CLIC- Note-627. [7] V. G. Vaccaro, Coupling impedance measurements: an improved wire method, INFN-TC [8] F. Caspers, C. Gonzalez, M. D yachkov, E. Shaposhnikova, H. Tsutsui, Impedance measurement of the SPS MKE kicker by means of the coaxial wire method, CERN- PS-RF-NOTE [9] International Linear Collider Reference Design Report, Vol. 3, at draft v1.pdf [10] 36