Coupler Design For The LCLS Injector L0-1 Structure
Zenghai Li, Lynn D. Bentson, David H. Dowell,
Cecile Limborg, John Schmerge, Liling Xiao
Abstract
The impact of multipole fields in the single-feed SLAC S-band structure is studied for the LCLS injector linac. Both the dipole and quadrupole fields were determined to significantly increase the beam emittance. A racetrack dual-feed coupler design will be used to replace the single-feed coupler in the L0-1 section to minimize the multipole field effect on beam emittance. The new coupler eliminates the dipole fields and minimizes the quadrupole fields to about 10 times smaller than that in the single-feed coupler. The parameters for mechanical drawing are presented. The sensitivity of the matching on geometry errors is provided.
Introduction
The photo injector for the LCLS is requiredto produce a 1-nC, 10-ps bunch witha normalized rms transverse emittanceof 1.0-µm. A photo-induced electron beam is produced in the 1.6-cell S-band RF gun by illuminating the cathode with a temporally shaped laser pulse. The electrons are accelerated to 6-MeV in the RF gun.Two3-m S-band accelerator structures, operating at 18-MV/m gradient, are required to drive the beam out of the spacecharge dominated regime. The SLAC 3-m S-band structure will be used for this booster acceleration. In the SLAC S-band structure, the RF power feed is through a single coupling hole (single-feed). Time dependent multipole fields in the coupler induce transverse kicksalongthe bunch, causing head-tail beam emittance degradation. Although the multipole field in the couplerisnot significant for the SLC beams, it is significant in the LCLS injector.
In the SLAC structures the measured asymmetries take the form of a linear amplitude and phase variation across the coupler cell in the direction of power flow. The longitudinal electric field can be expressed as shown in Eq. 1 [1] where E/E is approximately 0.1 and is approximately 1.5° with 2a = 0.7517 inches. However, no values for the non-linear terms of the amplitude or phase were reported. The values of the linear field and phase terms vary by about 30-40% between the entrance and exit coupler cells due to changes in coupler cell geometry.
1
The transverse variation of longitudinal electric field creates a transverse magnetic field which deflects the beam. A linear electric field variation leads to a magnetic dipole and a quadratic dependence creates a quadrupole field. The deflection due to the dipole is significant and was recognized before the SLAC linac was fabricated. In order to reduce the effect the coupler cells were offset to compensate the linear amplitude term with the natural Bessel function dependence of the cavity. This effectively reduced the amplitude term by a factor of 100 or more but did nothing to compensate the phase term. The resulting beam deflection for both the dipole and quadrupole term is shown in Fig. 2. The deflections are for a compensated SLAC structure (E/E = .001) and include the effect of a standing wave in the upstream half of the entrance coupler cell. The deflection for the quadrupole assumes a 1 mm beam size and a 10 ps long bunch is shown in red on the figure injected at -5.5°. An electron on crest is defined as 0 degrees phase. Both the dipole and quadrupole terms are computed from Eq. 1. Since the quadratic field and phase dependence for the SLAC coupler were not reported the quadrupole term computed from the linear variations most likely underestimates the real quadrupole term. The dipole term is almost entirely due to the phase term in Eq. 1. In the compensated SLAC structure the dipole term from the amplitude asymmetry is approximately one order of magnitude less than the dipole term from the phase asymmetry.
Figure 1The change in transverse momentum versus linac phase is plotted for both the dipole term and a quadrupole term assuming a 1 mm beam size. Also shown is a 10 ps long bunch for each case showing the different kicks received by the head and tail for a -5.50 lunch phase.
Due to the time dependent nature of the dipole and quadrupole fields, the head and tail of the bunch can be deflected by different amounts leading to an increase in the projected emittance. The estimated increase in the normalized projected emittance for both the dipole and quadrupole term is shown in Eq. 2 where px is the difference in momentum between the head and tail.
2
Since the change in transverse momentum for a relativistic beam does not depend on energy, the normalized emittance increase is independent of energy. However, the increase in projected emittance depends on the beam size and thus is typically most important in the injector where the emittance is small and the beam size large.
From Fig. 1 the difference between the head and tail momentum due to the dipole term is approximately .002. Thus for an initial emittance of 1 micron and a 1 mm beam size the final emittance is 1.4 microns. As discussed above the emittance increase due to the quadrupole term is likely to be underestimated due to the lack of knowledge of the quadratic field asymmetries. The emittance increase due to the quadrupole term can theoretically be compensated using solenoidal emittance compensation. However the emittance increase due to the dipole deflection can not. The solenoid can not compensate for a temporally correlated deflection which lead to offsets in phase space but can compensate for misaligned phase space ellipses.Thus it appears that the overall deflection must be reduced by about an order of magnitude to reduce the emittance growth to acceptable levels.
More rigorous studies on the tolerances on dipole and quadrupole time dependent kicks from the power flow in the entrance cell of L01, where the beam is large thus the head-tail effect is more important, have been performed using PARMELA. To simplify the simulations, the head-tail kicks were introduced at the entrance of the cell as a single kick. The dipole time dependent kick was represented by a linear angle offset from head-to-tail. The quadrupole kick was introduced as a linear quadrupole strength varying from head-to-tail. For both cases, we looked at the growth of the 80%-emittance (over 100 slices). The tolerance on the kick is set by limiting the emittance growth to 2%. For the dipole kick, the angle offset should not be larger than 120 micro-radiant from head-to-tail of a 10ps bunch as illustrated in Fig. 1. For the quadrupole kick, the quadrupole moment should not exceed 0.075 rad/m from head-to-tail of a 10ps bunch. Those two values set the tolerance to 60 micro-radiant for the dipole and 0.0375 rad/m for the quadrupole as we would like to leave the possibility open to run 20ps long pulses.
Figure 2Tolerances on dipole and quadrupole head-tail effects in the S-band accelerator. Simulated using PARMELA. Left: dipole field; Right: quadrupole field.
From Fig.1 the head-tail angle due to the dipole fieldin the input coupler of L0-1 is about 200 micro-radiant(6-MeV), which is a factor of 4 larger than the tolerance. Thus the dipole deflection in the coupler must be reduced by at least a factor of 4 in order to preserve the beam emittance.The quadrupole effect, in Fig. 1, is likely not estimated correctly due to lack of quadratic field information and need to be calculated numerically.Since the dipole term is mainly due to the phase asymmetry, the only feasible solution to reduce the dipole head-tail effect is to replace the single-feed coupler on the existing structure with a dual-feed coupler. The design of such a coupler is the main purpose of the work. The dual-feed schemetotally eliminates the dipole fields however do little to the quadrupole fields. A racetrack cell profile will be needed in the dual-feed design to minimize the quadrupole fields.
In this note, we will first present a full RF analysis of the dipole and quadrupole fields in the existing SLAC structures to understand fully the issues of the multipole fields in the single-feed coupler. We will then present the design and analysis for a new dual-feed racetrack coupler for the injector S-band structures.This dual-feed racetrack coupler will be used to replace the single-feed coupler in the L0-1 section. Dimensions of the dual-feed coupler will be provided for the mechanical design. Tolerance on design parameters will be analyzed.
3-D RF Simulation Method
Full 3-D RF simulation will be used to study the matching and multipole fields of the existing and new coupler designs. This section describes the code and method used in this work for the RF simulation and analysis.
1 Parallel code S3P
The finite element code S3P is used to simulate the coupler matching and to obtain the traveling wave fieldsto be used in the beam simulation. S3P is a parallel S-parameter simulation code developed in ACD, SLAC. It is implemented on multi-processor computer platforms(e.g., IBM-SP and Linux clusters) to take the advantage of massive memory and CPU power of these high performance computing machines, which allows to simulate large and complex geometries accurately and quickly.This code has been used in the design of X-band acceleration structureand RF components. It has been benchmarked with measurements of X-band coldtest prototypes.
2 Multipole analysis
The impact of the coupler fields on the beam dynamics is studied by analyzing the particle momentum change after traversing the coupler fields.The equation of motion
3
is integrated to obtain the momentum change (), which is directly related to the beam emittance. The momentum change is RF phase and initial position dependent.A number of particles of different initial positions will be traced and () calculated. Then a spatial harmonic decomposition is performed to obtain the multipole moments of the impact.
Multipole Fields in the Existing SLAC structure couplers
In this section we present the full wave simulation of the SLAC S-band structure couplers. Both the input and output RF power couplers in the SLAC 3-m structure feedis through a single coupling hole (single feed) as shown in Fig. 3. The coupler cells are racetrack shaped. The center of the racetrack cell is offset opposite to the coupling hole to compensate the dipole asymmetry due to the perturbationof the coupling hole. The center offset minimizes the dipole fields but enhances the quadrupole fields because the long side of the racetrack has to be oriented along the direction of the power coupler. In addition, the power flow from a single feed coupling hole induces phase variation across the coupler cell, which induces phase related dipole and quadrupole effects to the beam (even if the geometry asymmetry is compensated perfectly).
Figure 3 SLC structure input and output coupler cell geometries. The cell has a racetrack profile. The center of the cell is shifted to minimize the dipole fields.
1Coupler simulation
The parameters used to build the coupler model for S3P simulation are from a set of SLAC drawings. These drawing are appended to this note inthe Appendix.
The coupler perturbation is localized in the coupler and the adjacent cell. Beyond that, the fields are cylindrically symmetric through out the whole structure. Since we are interested in the 3D fields due to the coupler perturbation, we only need to include the coupler and the two adjacent cells in the simulation model. In the S3P simulations, a two-port network is required to calculate the S-parameters and the traveling wave fields.Two symmetric models were built for the input and output couplers respectively. Each modelis a reflected symmetry model of the coupler and two adjacent cells as shown in Fig. 4. In the beam dynamics studies for the input coupler, only the fields in the “port-1” side of the input coupler model are used. For the output coupler,only the fields in the “port-2” side of the output-coupler model are used.
Figure 4Symmetric model use for S3P simulation. A traveling wave is obtained by driving port-1 with a TE10 mode. Only one half of geometry is needed because of symmetry about the vertical plane.
2 Simulation results
The matching of the couplers was verified using S3P. The input coupler is well matchedat 2.856-Ghz with a reflection (S11) of 0.04, while the output coupler has a large reflection of 0.24.The output coupler isre-matched to reduce the standing wave content in the RF field. A reflectionof 0.04 was obtained by adjusting the opening of the coupling iris from 22.860-mm to 22.160-mm.It is worth to note that the SLAC structure couplers were tuned after they were built. The initial mismatch in the output coupler simulation is consistent withwhat was achieved on the actual structure.
The 3D traveling RF fields in the coupler models were obtained by driving the “port-1” with a TE10 mode. In Fig. 5 are plotted the transverse dipole and quadrupole moments of the coupler fields on the beam as functions of beam RF phase. The zero RF phase is the “crest” phase wherebeam gets maximum acceleration in this three-cell model. The crest phase in the full structure will be somewhat different because of the phase slippage due to low beam energy and the lower averaging coupler effect in the full length structure. The thicker line segments in Fig. 5 indicate the beams which are 10 degrees in length in RF phase. In table 1 are shown the head-tail momentum (()) and steering angle (()/) variations for a bunch accelerated on “crest”. Notice that in the real machine operation, the beam is off the “crest” by about -10 degrees. The head-tail effect in the real machine will be slightly different from the numbers shown in Table 1.
Figure 5 Head-tail effect of SLAC 3-m structure: left) input coupler; right) output coupler. The thicker line segment represents the 10-degree bunch which is on the RF crest in these plots. In the real injector operation, the beam is about -10 degrees off crest.
Table 1 Comparison of dipole and quadrupole head-tail effects in the SLAC 3-m structure input/output couplers. Bunch length=10degrees, Gradient=20MV/m
Input coupler / Output couplerBeam energy (g) / 10 / 130
Dipole: () / 2.610-3 / 1.010-3
Quad: D(g^)/m / 7.810-1 / 4.410-1
Dipole head-tail angle (rad) / 2.610-4 / 1.010-5
Quadrupole head-tail angle (rad/m) / 7.810-2 / 4.410-3
Both the dipole and quadrupole head-tail effects of the single-feed input coupler are found too large for the LCLS injector section L0-1. It is thusnecessary to use a more symmetric coupler design for the input of L0-1 to minimize thehead-tail emittance degradation.
In the output coupler of L0-1, the head-tail effects (())are about half of that in the input coupler. In addition, because of the 10-times higher beam energy at the output coupler, the beam size is damped by a factor of more than 3, assuming beta function does not very too much in the structure. The head-tail emittance growth is about 6 times smaller. Similarly in the accelerator section L0-2 and accelerator sections down stream, the beam size is adiabatically damped so are the head-tail effects.It is thus adequate to use the existing single-feed couplerfor the output of L0-1 andfor the structures down stream.
Dual-feed input coupler for L0-1
1 Coupler design and optimization
In this section we present a dual-feed design for the accelerator section L0-1 to minimize the coupler multipole fields.The dual feed coupler eliminates the dipole fields by symmetry. A racetrack coupler cell, with the coupling hole on the long side, is needed to minimize the quadrupole fields. One additional improvement in the new design is to round the edges of the coupling irises. The rounding of the irises minimizes field enhancement and RF heating. Although there were no problems encountered in the SLAC structures due to sharp coupling holes edges,it is evident in the X-band high power test that the sharp edges in the coupling hole have caused successive pulse heating and breakdown damage. As a result, all the new X-band couplers are designed with no sharp edges, and the structure high gradient performance is improved greatly. With this in mind, it is believed beneficial to have the coupling irises rounded in the new design. A sketch and a cutaway view of the dual-feed racetrack coupler for L0-1 are shown in Fig. 6.The radius of the rounding on the coupling iris is chosen to be 1-mm. The two (+)s mark the centers of two racetrack arcs. The separation of these two arc centers need to be adjusted to reduce the quadrupole field. The iris opening and the arc radius are the parameters used for matching the coupler. The design was done iteratively between adjusting the arc separation for quadrupole field and adjusting the iris and the arc radius for matching. For a given arc separation, the coupler is matched and quadrupole field is analyzed. After a number of iterations, we reached a design that has a matching reflection of 0.02 and quadrupole field about 10 times smaller than the SLAC single-feed coupler, see Fig. 7 and Table 2.
Figure 6Dual-feed coupler with racetrack cell profile to minimize dipole and quadrupole fields.
Two more coupler configurations were studied for comparison. One is a dual feed with a cylindrical cell profile (cylindrical dual feed). The other is a dual-feed with a cylindrical cell plus two slots, the same width as the coupling iris, 90 degrees away azimuthally from the coupling iris to compensate the quadrupole effects (cross dual feed). In Fig. 7 and Table 2 are shown the quadrupole moments of these designs for comparison.It is clear that the racetrack dual-feed coupler is least in quadrupole fields.