SPARC-BD-3/6 SPARC-RF-3/3 25 Noveber 23 LONGITUDINAL AND TRANSVERSE PHASE SPACE CHARACTERIZATION D. Alesini, C. Vaccarezza, (INFN/LNF) Abstract The characterization of the longitudinal and transverse phase space of the bea provided by the SPARC photoinjector is a crucial point to establish the perforance quality of the photoinjector itself. By eans of an RF deflector and a dispersive syste, the six diensional bea phase space can be analyzed. In this paper we present the principle and the siulation results of the easureents, together with a detailed description of the RF deflector design.
2 1 INTRODUCTION The characterization of the longitudinal and transverse phase space of the bea is a powerful tool in order to verify and tune the photoinjector perforance. With the use of an RF deflector it is possible to easure the bunch length [1,2]; adding a dispersive syste the longitudinal bea phase space can be copletely reconstructed. The longitudinal bea distribution can be projected along a given transverse coordinate at a detector flag and, using the orthogonal transverse coordinate distribution, both the horizontal and vertical bea eittances can be easured with the quadrupole scan technique. A scheatic layout of the easureent is reported in Fig.1. Q D 3 F2 Q D 4 Q D 6 F3 Q T 1 Q T 3 D1 Linac 3 Q T 2 RFD Q D 1 F1 Q D 2 Q T 4 Q T 6 F Q T 5 D2 Q D 5 toundulator agnetic chicane (phase III) Q T = transfer line quads Q D = dogleg quads RFD = RF deflector D = dogleg dipoles F = flags FIG. 1: SPARC easureent layout for high energy bea characterization. In Fig. 2 the effect of the RF deflector is illustrated: the RF deflector voltage (the integrated transverse kick) is null in the longitudinal center of the bunch and gives a linear transverse deflection to the bunch itself. If we consider the bea distribution and a drift space of length L after the deflector, the transverse kick results in a transverse displaceent of the centroid of the bunch slice. This displaceent is proportional to the slice longitudinal offset L B, and RF voltage according to the expression x B = p f RF LLBV^ ce / e (1) where f RF is the frequency of the deflecting voltage, V^ is the peak transverse voltage, and E/e is the bea energy in ev units. More coplicated expressions result when one considers agnetic coponents instead of a siple drift space between the deflector and detector. Equation (1) shows that the longitudinal bunch distribution can be obtained by easuring the transverse bunch distribution at the position z s.
3 DEFLECTING VOLTAGE s x x B L B x z s z DEFLECTOR BUNCH L SCREEN LINAC DEFLECTOR ONDULATOR. FIG. 2: Bunch length easureent scheatic setup using an RF deflector. As illustrated in Fig. 2 the transverse distribution of the bunch at the position z s is the convolution between the displaced slices and the proper transverse slice sizes at the position z s. In order to easure the bunch length with the proper accuracy, the displaced position x B has to be bigger than s. The resolution length (L res ) can be defined, therefore, as the relative x slice longitudinal position that gives, on the screen, an x B equal to s x. By use of Eq. (1) we can calculate the transverse voltage V^ necessary to achieve a certain resolution: V ^ s xce / e = pf LL RF res (2) A sketch of the coplete longitudinal phase space easureent setup is shown in Fig. 3. In this scenario, the bunch is vertically deflected by the RF deflector and horizontally by a agnetic dipole. The dispersion properties of the dipole allow to copletely characterize the energy distribution of the bunch and the total longitudinal phase space can be displayed on the screen. x x (long. Pos.) y L B z y ( D E/E) DEFLECTOR DIPOLE SCREEN. FIG. 3: Longitudinal phase space easureent setup using an RF deflector and a dipole agnet.
4 The transverse phase space characterization is obtained easuring the bea slice eittance in both the transverse planes. The slice eittance is the transverse eittance of a short tie interval (slice) of the icrobunch. It can be easured using a bea with a linear energy-tie correlation, or chirp; the chirp is cobined with the quadrupole scan technique to deterine the eittance of the slices along the bunch [3-5]. This type of energy-tie correlation can be provided by the RF deflector or by use of the dispersive syste. Using the RF deflector the horizontal slice eittance e x can be easured either on the transfer lines or on the dogleg, at the flags F and F3, respectively. The bea eittance can be calculated by the following expression: s 11 s 22 -s 2 12 = e 2 (3) where the easured quantities s 11, s 21 and s 22 are the second oents of the horizontal trace space. This relationship is indicated in copact for through the equation of an n- diensional ellipse written as u T s -1 u =1 (4) where u and u T are the coordinate vector and its transpose, and s is a syetric atrix.the first two quads after the linac sections, Q T 1 and Q T 2, are used in this case for the quadrupole scan: the bea horizontal size at the the screen (F,F3) is varied keeping constant the vertical one. The easureent results are fitted following the equation s screen 11 = R 2 s 11 o s 11 + 2R 12 R 11 o 12 + R 2 s 12 o 22 (5) screen where s 11 is the horizontal bea rs size easured at the screen, and R 11 and R 12 are the first two eleents of the atrix governing the bea transport fro the first scanning quadrupole to the screen considered. With the dispersive syste the sae two quads are used to vary the vertical bea size at the location of the flag F2 with an opportune value of the horizontal dispersion. The third linac section is dephased of about 3 o to produce the desired energy chirp. The easured values of the rs vertical bea size are fitted to obtain the vertical bea slice eittance. 2 SIMULATIONS RESULTS 2.1 Longitudinal phase space easureent Using Eqs. (1) and (2) it is possible to calculate the total transverse diensions of the bunch as a function of the deflecting voltage V^ and needed deflecting voltage V^ as a function of
5 L res. The results are plotted in Figs. 4(a) and 4(b), assuing L B =4, E/e=15 MV, L=2 and s = 3. x. FIG. 4: (a) total transverse diensions of the bunch as a function of the deflecting voltage V^; (b) deflecting voltage V^ as a function of L res. Fro these considerations, as well as a desire to itigate the total power needed, a voltage V^=1. MV has been chosen for the RF deflector. A 15k particle bea obtained fro PARMELA siulation at the end of the linac section has been tracked with the ELEGANT code along the SPARC transfer lines. The iages of the bea obtained at the RF deflector location and at the screen location, F, are shown in Figs. 5 and 6. The results of the data analysis are shown in Fig 7 where the vertical projected and the longitudinal distributions of the bunch are displayed. The value of s z as obtained by applying Eq. (1) and by the longitudinal analysis of the raw data obtained fro ELEGANT tracking agree with an error less than 1%. FIG. 5: Bunch transverse distribution at the RF deflector location.
6. FIG. 6: Bunch transverse distribution at the RF deflector location. 15 1 5 2 1.5 1.5 -.5-1 -1.5-2 x 1-3 FIG. 7: Above: the longitudinal bunch distribution as projected by the RF deflector on the vertical coordinate of the screen F; below: the sae bunch longitudinal distribution vs. tie.
7 The iages collected on the dogleg at the screen located in F1 show the coplete reconstruction of the longitudinal phase space as shown in Figs. 8 and 9 where the tieenergy (t,p) distribution is replicated in the transverse plane (y,x). The reconstructed rs energy spread value is in very good agreeent with the real one. The slice analysis is under study to take into account all the relevant effects. FIG. 8: Bunch longitudinal distribution vs tie at F1. FIG. 9: Bunch transverse distribution at F1
8 2.2 Transverse phase space To easure the bea slice eittance in the horizontal plane the RF deflector can be used scanning the bea rs size at the screen locations F and F3, where two different values of iage resolution can be achieved for the iniu horizontal rs size reconstruction. For the vertical eittance the dispersive syste can be used with the bea iage being exained at the screen location F2. In Figs. 1 and 11 the optic functions of the SPARC transfer lines and dogleg are reported for the easureent setup of the horizontal eittance. F FIG. 1: SPARC transfer lines optic functions for the horizontal quad scan at F. The origin of the longitudinal coordinate corresponds to the exit of the second linac section. F3 FIG. 11: SPARC dogleg optic functions for the horizontal quad scan at F3. The origin of the longitudinal coordinate corresponds to the exit of the second linac section.
9 In Fig. 12 the bea horizontal slice eittance is given for the two siulated easureents at F (left) and F3 (right), respectively. For the top figures, the result of the teporal analysis of the raw data is reported for the two cases; those below show the reconstructed horizontal slice eittance. The ain difference between the results obtained scanning at F or F3 is the inu value of the rs bea size as can be seen in Fig. 13, where the curves refer to the new SPARC working point optiization (1.1 nc). This aspect provides a tool to investigate a wide range of bea eittance values without loosing the easureent accuracy. ) d a r ( g e x 4 3.5 3 2.5 2 1.5 1.5 ) 3 d a 2.5 r ( g e x 1.5 2 4 6 8 1 12 14 16 18 slice nuber 3.5 2 1.5 4 x 1-6 ) d a r ( g e x 4 3.5 3 2.5 2 1.5 1.5 3.5 ) d 3 a r 2.5 ( 2 g e x 1.5 2 4 6 8 1 12 14 16 18 slice nuber 1.5 4 x 1-6 18 16 14 12 1 8 slice nuber 6 4 2 2 4 6 8 1 12 14 16 18 slice nuber FIG. 12:: Reconstructed horizontal bea slice eittance (in -rad) as a function of slice nuber with the bea size scanning at F (left), and at F3 (right). The a) curves (above) is the horizontal eittance as calculated by slicing the bea along the teporal coordinate, the b) curves (below) are the result of the two quadrupole scan at the two screen locations..25.25 ) ( s r x.2.15.1.2 ).15 ( s r x.1.5.5 2 4 6 8 1 12 14 16 18 2 slice nuber 2 4 6 8 1 12 14 16 18 2 slice nuber FIG. 13: Miniu horizontal rs bea size (c) at the two screen locations: F (left), and F3 (right) during the quadrupole scan.
1 3 RF DEFLECTOR DESIGN The siplest and ore efficient ulti-cell deflecting structure that can be used to deflect the bunch is a standing wave structure operating in the p -MODE. In Fig. 14 it is shown, as an exaple, a siple 5-cells cavity with bea pipe tubes. The external radius (b) has been chosen in order to tune the resonant frequency of the p -MODE to 2.856 GHz, the internal radius (a) is equal to the bea pipe radius (2 ), the cell length (d) is equal to c/2f RF to synchronize the bunch passage and the deflecting field. The iris thickness (t) has been chosen as a reasonable value of 9.5, considering that it is not a critical diension in ter of sensitivities. The dispersion curves of the single cell as obtained by MAFIA 2D [6] siulations with b=6 are reported in Fig. 15. The deflecting p -MODE has a frequency equal to 2.856 GHz, while the nearest onopole and dipole odes are far away fro the deflecting ode. The deflecting voltage V ^ is related to the dissipated power in the cavity P RF (equal to the input power if the coupling coefficient between the generator and the cavity is equal to 1) and the transverse shunt ipedance R^ by the relation: V 2P ^ = RF R^ (6) The total transverse shunt ipedance R ^, quality factor Q, and frequency separation with respect to the nearest odes D f, as a function of the nuber of cells n, has been calculated by MAFIA 2D. The results of this study are reported in Table 1. The transverse shunt ipedance scales approxiately as R ^ @.5MW * n while the quality factor is practically independent of n. The peak surface electric field E P in the structure has been found to scale approxiately as: ÈMV EP Í @ 9 Î P RF [ MW] n (7) Therefore with an input power P RF =2 MW we obtain E P @6 MV/ with 5 cells and a arginally unacceptable E p @13 MV/ with 1 cell. The previous results allow us to choose the nuber of cells for the deflecting structure. The choice can be optiized considering the following considerations: a) the available transverse deflecting voltage for a given input power; b) the available space in the SPARC transfer line; c) the ode separation with different nuber of cells to avoid probles of ode overlapping; d) the axiu acceptable surface peak electric field to avoid probles related to high field intensities, discharges and so on. The 5-cell deflecting structure fulfills all of the stated requireents. In fact, it allows to operate with a very low input power P RF 2MW obtaining conteporary low peak surface
11 electric field and resolution length of the order of ~25 at P RF =2MW. These paraeters perit easureent of the longitudinal bea profile with good accuracy, even considering the possibility of longitudinal copression factors of up to 2. Moreover the operation at low input power ( 2MW) allows to siplify the power line design as discussed below. TAB 1: Deflecting cavity properties obtained by MAFIA 2D siulations as a function of the nuber of cells. Nuber of cells Total length cells [] Transverse Ipedance [ M W ] Quality factor Bandwith [khz] Nearest ode frequency separation [MHz] 3.16 1.5 171 167 25 5.26 2.5 167 171 6 9.47 4.5 169 169 1.5 d b a t FIG. 14: The transverse profile of the 5-cell deflecting cavity. p-mode FIG. 15: Single cell dispersion curves of deflection-ode standing wave structures obtained by MAFIA 2D siulations.
12 3.1 5-cell RF deflector design procedure 3.1.1 2D profile study The 2D profile of the 5-cell RF deflector has been studied using the MAFIA 2D code. The frequency sensitivities of the single cell profile with respect to the diensions are reported in Table 2. The siulated 5-cell profile is reported in Fig. 16 with the diensions shown in Table 3. The radius of the cells connected to the bea pipe tube in this design has been changed in order to achieve a field flatness of 3%. The on-axis agnetic field profile in the structure is plotted in Fig. 17 and the results of the MAFIA siulations in ter of resonant frequency, transverse shunt ipedance and quality factor are reported in Table 4. These calculated quantities are also copared with the HFSS [7] results discussed in the next paragraph. To evaluate the sensitivities of the resonant frequency and field flatness as a function of the single cell diensions, a battery of siulations have been perfored. The results are reported in Table 5 and Fig 18 for the ost critical paraeter b. Fro this study, it is possible to conclude that errors in the cells achining of the order on 1-2 give frequency errors of the order of 1 khz and field errors of few percent. These errors can be easily copensated by a proper tuning procedure. TAB 2: Frequency sensitivities of the single cell profile with respect to the cell diensions. Diension noinal value [] sensitivity [khz/ ] a 2. -19 b 6. -43 t 9.5 1.2 d 52.48 1.8 TAB 3: Diensions of the 5-cell structure. Diension value [] a 2. b2=b3 59.97 b1 6.67 t 9.5 d 52.48 TAB 4: Siulation results of the 5-cells deflecting cavity (coparison between MAFIA 2D and HFSS) MAFIA HFSS Frequency [GHz] 2.85699 2.85467 Q 168 164 [ M W ] R^ 2.47 2.43
13 TAB 5: Resonant frequency sensitivity with respect to the external radius b. Diension sensitivity [khz/] b1 8.6 b2 1.8 b3 d b1 b2 b3 t a FIG. 16: 5-cells deflecting cavity siulated by MAFIA 2D. FIG. 17: Absolute value of the agnetic field for the 5-cells cavity obtained by MAFIA 2D siulations. FIG. 18: Relative agnetic field sensitivity with respect to the external radius of the cells.
14 3.1.2 3D profile study The 3D siulation study of the deflecting ode structure has been perfored using HFSS. The coparison between the 2D and 3D results is shown in Table 4 where we consider the 5- cell structure without coupler. The coupler design has been chosen to adapt a rectangular waveguide coupler feeding the central cell of the structure. The HFSS siulated structure is plotted in Fig. 19. After soe optiization and re-tuning of the central coupler cell we have obtained the result plotted in Figs. 2(a) and (b) in ter of field flatness and reflection coefficient at the input port respectively. The obtained coupling factor b and the transverse shunt ipedance are equal to.94 and 2.11 M W, respectively. A coplete investigation has been perfored in order to find the ode separation between the desired deflecting ode and the nearest ode within the pass-band. The result is suarized in Table 6. It is iportant to reark that the nearest odes are not excited by the coupler and can, therefore, perturb only arginally the deflecting field. The nearest ode that can be excited by the coupler is the p /2 deflecting ode, whose agnetic field profile is shown in Fig. 21. Concerning the tuning syste, the siulations perfored on the 3D single cell of Fig. 22 shows that a cylindrical tuning rod of r=5 (siilar to those found in the RF gun) gives a sensitivity of 55 khz/. This is enough to easily copensate any possible achining error. TAB. 6: Frequency separation between the deflecting ode and the nearest unwanted odes. D f Excited by the [MHz coupler ] Deflecting ode tilted polarity (9 deg.) NO 6.5 3 4p ode polarities deg. NO 5.4 3 4p ode polarities 9 NO 5 p /2 ode YES 2 FIG. 19: 3D HFSS siulated structure with coupler.
15 (b) (a) FIG. 2: HFSS coupler siulation results: a) reflection coefficient at the input port; b) on-axis agnetic field profile. FIG. 21: Magnetic field of the p/2 deflecting ode excited by the coupler. FIG. 22: 3D single cell with tuning syste siulated by HFSS.
16 3.2 RF deflector power feed syste The 2 MW input power needed to feed the structure can be split out fro the first klystron waveguide feed with a 1 db directional coupler, as illustrated in Fig. 23. The circulator and the directional coupler shown assure that every reflected power fro the deflector does not interact with the power feeding the RF gun. Moreover the high power switch is included to allow the deflecting field to be copletely turned off. Because of the reduced power needed for the structure it is possible to siply eploy a waveguide syste with air-fill, thuis reducing the costs of the entire power feed syste. FIG. 23: Sketch of the RF deflector power feed syste. 4 CONCLUSIONS In this paper we have discussed the ethods to characterize the longitudinal and transverse phase space at SPARC. They are based on the use of an RF deflector that allows to easure the bunch length or the coplete longitudinal phase space by adding a dispersive syste. Using the quadrupole scan technique both the horizontal and the vertical bea slice eittances can be easured. The siulations ade by the ELEGANT code have shown the feasibility of this diagnostic syste. In the paper we have also discussed the RF deflector design ade by the use of the e.. codes MAFIA and HFSS. It is a 5 cells SW structure working on the p -MODE at 2.856 GHz and feeded by a central coupler with b =1. Since the shunt ipedance is ª 2.5MW and the axiu input power is 2 MW, it is possible to obtain a resolution length of the order of 25.
17 5 REFERENCES [1] P. Ea, et al., A Transverse RF deflecting structure for bunch length and phase space diagnostics, LCLS-TN--12, 2. [2] G.A. Loew, O,H Altenueller, Design and applications of RF deflecting structures at SLAC, PUB-135, Aug. 1965. [3] D.H. Dowell et al, Slice Eittance Measureents at the SLAC Gun Test Facility, SLAC-PUB-954, Septeber 22 [4] J.F. Scherge et al, Transverse-eittance easureents on a S-band photocathode RF electron gun, Nucl. Instr. & Meth. A 483, 22, pp. 31-34 [5] X. Qiu et al, Deonstration of Eittance Copensation through the Measureent of the Slice Eittance of a 1- ps Electron bunch, Phys. Rev. Lett. 76, 2, 1996, pp. 3723-3726. [6] www.cst.de. [7] www.ansoft.co.