The coaxial coupled linac structure

Nuclear Instruments and Methods 193 (1982) 437-444 North-holland Publishing Company

437

THE COAXIAL COUPLED LINAC STRUCTURE J.-P. LABRIE * and J. McKEOWN Accelerator Physics Branch Research Company, Chalk River Laboratories, Chalk River, Ontario KOJ IJO, Canada

Received 28 August, 1981

A new type of biperiodic accelerating structure is described. The coaxial coupled structure makes use of coaxial cavities isolated from direct beam excitation to couple power between adjacent accelerating cells. The advantages of the 7r/2-mode are therefore available for application in storage rings at a loss in shunt impedance of 7%. Parasitic modes in on-axis coupled biperiodic systems are reduced by half and excitation of beam blowup (BBU) modes by a simulated off-axis beam show that the sensitivity of the coaxial coupling cells to BBU modes is two orders of magnitude smaller than for on-axis coupling cells.

1. Introduction Recent efforts in linear accelerator structure research have concentrated on improving the conversion of rf power into beam power by increasing the efficiency of the accelerating mode. Many shaped cavity designs [ 1 ] have resulted from this work. Additional studies for high energy storage rings have also evaluated the power losses from beam-cavity interactions and concluded that only relatively simple shapes are tolerable if beam driven parasitic modes are to be avoided. The relatively simple n-mode structures are preferred for this application. In linacs and microtrons, where bunches are more numerous but much smaller, the effect of beamcavity interactions is to reduce more the beam quality than the efficiency. Beam loading in controlled standing wave structures increases the field tilt from the rf drive hence changing the longitudinal emittance of the beam. This has generated considerable interest in the disc-and-washer structure [2] where high intercavity coupling of a ~r/2-mode system can reduce this effect. Beam excitation of transverse deflecting modes [3] (beam blow-up (BBU) modes) in cavities leads to a deterioration of beam optics and loss of particles in the structure walls. These modes are important in all accelerators but are of particular concern in circular accelerators because they are regenerative. At the Chalk River Electron Test Accelerator, a * Visiting Scientist from Universit~ de Montreal. 0029-554X/82/0000-0000/$02.75 © 1982 North-Holland

study of these problems is in progress [4] and possible solutions are being investigated. A new structure, the coaxial coupled structure has been developed which combines the advantages of the accelerating field stability of the 7r/2-mode systems [5], and the mechanical simplicity of the on-axis coupled structure [6]. High coupling is possible and sensitivity to higher order mode excitation is reduced. It is believed that the coaxial coupled structure will have applications in linacs, electron storage rings and microtrons. Its only disadvantage is a 3% increase in the overall cost when compared with the on-axis coupled structure arising from an increase in the mass of copper required.

2. Coaxial coupled structure description The coaxial coupled structure is a combination of the ring coupled structure [2] and the on-axis coupled structure [7]. As shown in fig. 1, direct coupling to the beam is eliminated by joining the nose cone of adjacent accelerating cells in the on-axis coupled structure hence precluding excitation of the TMolo mode in the coupling cell. However, the TEM mode can be excited by increasing the radius of the coupling cell and magnetic coupling is possible through. slots situated near the nose cone. The overall radius is less than that of the ring coupled structure but larger than the on-axis coupled structure. At the low frequencies of most operating electron storage rings, the increased radius may be considered a significant

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penalty but the more stable biperiodic accebrating system can be used without higher order mode excitations in the coupling cells. Axial symmetry is still preserved, hence the magnetic and electric field distributions along the web separating the accelerating cell from the coupling cell in a coaxial coupled cavity can be calculated with the two-dimensional rf cavity evaluation computer code SUPERFISH [8]. Fig. 2 shows magnetic and electric field distributions in the coaxial coupled structure. The fundamental TEM-like mode (with X-~ 21h a), where b and a are, respectively, the outer and inner coupling cell radii) excited in a coaxial coupling cell allows magnetic coupling to the accelerating cell through coupling slots located at the inner radius (a) of the coaxial coupling cell and above the nose cone of the accelerating cell where the magnetic field is

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J.-P. Labrie, J. McKeown /Coaxial coupled linac structure of 0.09 mm -1 as the web thickness is increased. This compares with the decay constant of 0.06 mm -1 calculated with SUPERFISH.

3.2. Higher order mode sensitivity There are basically two types of higher order modes. Axially symmetric modes which cause bunch lengthening and reduce the beam luminosity [10], and BBU modes excited by the passage of an off-axis beam through cavities causing beam loss and incoherent synchrobetatron oscillations [11] in circular machines. These are predicted to limit the beam current for both high and low Q cavities. Design studies of high energy storage rings such as the proton-electron-positron (PEP) and the large electron-positron (LEP) storage rings have prompted much theoretical and experimental work in the evaluation of power losses resulting from beam-cavity interactions. Higher order mode excitation by a beam bunch reduces rf cavity efficiency and consequently increases the rf power requirements. In the PEP [12] rf system, higher order mode losses excited by the beam in the structure itself dominate by a factor of two over the losses in the remainder of the vacuum chamber components, adding an additional 0.5 MW to the 2.2 MW dissipated in the fundamental mode for 15 GeV operation. As shown in the appendix, the relative sensitivity in terms of beam disturbance to direct cw beam excitation of higher order modes in cavities is given by the ratio of their Q. For an on-axis coupled structure, the Q of a coupling cell is about 10% that of an accelerating cell. Since the transit time through a coupling cell is one order of magnitude smaller than the transit time through an accelerating cell, the higher order mode field amplitudes are expected to be similar in both ceils and hence the energy loss parameter [13] for an on-axis coupling cell to be 10% that of an accelerating cell. Therefore it is expected that removing the coupling cell from direct beam-cavity interactions will reduce the higher order mode sensitivity by 10%. Axially symmetric mode sensitivity is calculable, but the sensitivity of a cavity to BBU modes can only be examined experimentally. (1) Axially symmetric modes. Predictions of the total energy loss to the excitation of axially symmetric modes resulting from beam-cavity interactions have been made with the computer code BCI [14] which solves numerically Maxwell's integral equations in the time domain for modes with cylindrical sym-

439

metry. For the Canadian high energy electron ring (CHEER) on-axis coupled structure, a total energy loss parameter of 0.29 V/pC was found for the accelerating cell and 0.03 V/pC for the on-axis coupling cell for a beam bunch with a r m s bunch length of 20 mm [15]. This result shows that the energy extracted from a bunch to excite axially symmetric modes in the coupling cell is 10% of the energy extracted in the accelerating cell and is consistent with the theory given in the appendix. (2)Beam blow-up modes. The main contribution to BBU modes in linear accelerator structures comes from the excitation of the TMll0-1ike modes by an off-axis beam. A hybrid structure, shown schematically in fig. 4, composed of two on-axis coupled half cavities and of two coaxial coupled half cavities, and both haing an accelerating mode frequency, fo, of 1.35 GHz, was constructed to measure beam excitation of the TM110-1ike modes in the accelerating and coupling cells. The segments were made of aluminum for low power tests only. The profiles of the accelerating cells of both type of cavities were identical. In all cases, coupling slots had the same width and same arc length. The coupling constant was 2.49% for the coaxial coupled structure and 2.06% for the on-axis coupled structure. Web thicknesses were identical for both types of structure. A direct comparison of BBU sensitivity of the two types of structure was therefore possible. Previous beam experiments [16] at this laboratory show that the strength of the TMx~o-like mode in a cylindrical cavity is determined by the product of the displacement of the beam from the symmetry axis and the magnitude of the square of the beam current.

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In the measurements to be described, excitation of the BBU modes by an off-axis beam is sinmlated by short pulses of current in a thin conducting wire (0.127 mm diameter) displaced from the structure symmetry axis [ 17]. The experimental arrangement is shown schematically in fig. 5. Current pulses are obtained from an oscillator sweeping a frequency domain around the known frequency (~1.69 fo) of the TMllo-like modes. Mode amplitudes are measured with magnetic probe loops and crystal detectors. As expected the normal accelerating mode is grossly disturbed by this technique but careful measurements show that provided the wire does not run along electric field lines of a particular mode, disturbance of that mode is negligible. Experiments with a brazed copper on-axis coupled system are in progress [181 and beam experiments are planned. Resonance frequencies of the TMllo-like modes in the two different structure cells were determined by exciting individual cells with a loop placed on the cell axis. The dashed and smooth lines in fig. 6 represent the magnetic field orientation of the modes in each cell. The coupling slots remove the azimuthal degeneracy of the TMll0-1ike mode in the cavity midplane. Rotation of the loop can excite two different modes simultaneously at two different frequencies: one mode has a symmetry plane parallel to the coupling slot axis while the other has a symmetry plane perpendicular to the slot axis. A measure of the relative difficulty of exciting these modes in the different cells of the hybrid structure is obtained by sending known current pulses along a wire displaced off-axis and measuring the TMllo-like mode amplitude in the different cells. As predicted from the theory in the appendix, the amplitudes of the TMllo-like mode excited in the accelerating and in the on-axis coupling cells were similar.

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In the coaxial coupling cell, TMllo-like modes can only be excited through the coupling slots and tile measured amplitude was two orders of magnitude smaller.

4. Beam blow-up mode distributions and propagation Properties of the BBU modes excited in a coaxial coupled and in an on-axis coupled structure were measured. The amplitudes of the TMllo-like modes excited by a pulsed off-axis wire were measured as a function of the wire displacement from the structure axis. The amplitude of the mode varies linearly with wire displacement as can be seen from fig. 7. As the wire displacement is increased, it effectively shunts the mode's electric field lines, destroys the Q of the mode and changes its frequency. This produces a saturation of the mode amplitude in fig. 7. The saturation point occurring at a smaller wire displacement in the case of the on-axis accelerating cell, suggests that the field lines extend closer to the structure axis than in the coaxial coupled accelerating cell. This may be due to the radial position of the coupling slots and in turn suggests that the TMllo-like mode can be more easily excited in an on-axis coupled accelerating cell. The electric field distribution of the TMllo-like modes in the on-axis coupled (fig. 8) and in the coaxial coupled (fig. 9) were measured radially using

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a dielectric bead (19). These measurements show firstly that the field distribution of the TM1 ~o-like mode in the two types of accelerating cells are similar, secondly that the field distributions remain the

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same if the cells are excited by an off-axis wire or by a loop placed on the cells' axis, and thirdly that bead pull measurements were not sufficiently sensitive to detect a difference in the field distribution in the beam hole area as suggested from the results of fig. 7. Results from radial bead displacement in the coupling cells are shown in fig. 10. For the coaxial coupling cell, the field distributions o f the TM1 lo-like modes are identical with an electric field maximum located at a + ( b - a)/2 where b and a are, respectively, the outer and inner radii of the cell. For the on-axis coupling cell, the field distributions of the two TMlxo-like modes are different. The maximum negative frequency shifts which correspond to the maximum electric field are displaced towards the coupling slots for the TM~lo-like mode with a symmetry plane perpendicular to the coupling slot axis. The coupling slots act as a sink for the electric field lines and electric coupling of this mode to the equivalent mode with the same symmetry plane in the accelerating cell of the on-axis coupled structure has been observed. It is known [20] that the frequency of the coupling cell is strongly dependent on the size of the coupling slot, hence it is important that any selection of first neighbour coupling by

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choice of the length of the coupling slot be tnadc with full knowledge of the two frequencies of the BBU modes. As shown in fig. 6, the frequencies of tile 'FM~~olike mode in the coaxial coupling cells are well separated from those in accelerating cells, thus inhibiting BBU mode propagation in a coaxial coupled structure. Table 1 gives a summary of properties of different types of linear accelerator structures. Because of its high shunt impedance and high coupling, the diskand-washer structure represents an improvement in terms of rf efficiency but at the expense of a larger overall radius and more complex assembly procedures. The on-axis coupled structure, the ring coupled structure and the coaxial structure are variants of the side-coupled structure [9]. These structures have identical accelerating cells and thus approxinmtely the same shunt impedance. There is however a penalty of 7% for the increase in effective web thickness by the coupling cell.

Table 1 Linear accelerator structures (1.35 GHz, ~ = 1) Structure

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Ring coupled

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5

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18

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difficult

medium difficulty

easy

medium difficulty

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difficult

difficult

easy

medium difficulty

easy

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2.5

2

2

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4.5

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high

fair

low

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unknown

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unknown

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no propagation

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9.0

J.-P. Labrie, J. McKeown / Coaxial coupled linac structure 5. C o n c l u s i o n s

Parasitic modes excited in biperiodic systems can be reduced if direct beam-cavity interaction of the resonant coupler is eliminated. Measurements have shown that the sensitivity of the coupling cells in an on-axis coupled structure to beam blowup modes is 10% that of an accelerating cell. The frequency proximity of the TMllo-like modes in on-axis coupling and accelerating cells allow electric coupling of the mode with a symmetry plane perpenaicular to the coupling slot axis and hence beam blowup mode propagation between neighbouring cells is possible. For identical coupling slot width and arc length, 21% more first neighbour coupling is obtained with the coaxial coupled structure. Excitation of parasitic modes in the coaxial coupling cells by coupling to the beam through the coupling slots was shown to be two orders of magnitude smaller than in on-axis coupling cells and beam blowup mode propagation in the coaxial coupled structure is not observed. As both structures have equal merit in terms of mechanical simplicity and shunt impedance, the coaxial coupled structure is preferred for applications where beamcavity interactions are important.

Appendix

Relative sensitivity to higher order mode excitation o f on~xis accelerating and coupling cells

where Q = coU/P is the usual definition of the quality factor with U being the stored energy of the mode, E z = eTkx and T is the transit time factor. The value of eT is the measure not only of the cavity sensitivity to the mode excitation but, more completely, the actual disturbance of the beam. The electric field of the higher order mode in a cavity after the passage of a bunch of charge q is given by [11]

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(l)

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(2)

1 ox (

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(3)

where r is the time between successive bunches. For cw linear accelerators r = 1/fo. The experimental factor comes from the field decay between bunch passages. Since the Q of an accelerating and of a coupling cell is large (respectively about 20 000 and 2000), the exponential factor is expanded to its first order term and eq. (3) becomes

Since r'o/Q depends only on the frequency of the mode and because of the frequency proximity of a Tmno-like mode in an accelerating and in a coupling cell, the ratio of sensitivity to direct beam excitation of higher order modes of a coupling cell to that of an accelerating cell is given by (eT)c _ Qc

(eY)A QA If cylindrical accelerating and coupling cells are assumed, their relative sensitivity to direct excitation of higher order modes can be readily expressed in terms of the resulting beam disturbance. The transverse shunt impedance of a higher order mode is given by [21]:

443

(5)

References

[lJ J.J. Manca, Los Alamos Scientific Lab. rep. no. LA7157 (1978). [2] V.G. Andreev, V.M. Belugin, V.G. Kulman, E.A. Mirochnik and B.M. Pirozhenko, Proc. of the 1972 Proton Linac Conf. (Los Alamos Scientific Lab. rep. no. LA-5115, 1972)p. 114. [3] H. Herminghaus and H. Euteneuer, Nucl. Instr. and Methods 163 (1979) 299. [4] G.E. McMichael, J.S. Fraser and J. McKeown, Proc. of 1979 Linear Accelerator Conf. (Brookhaven National Lab. rep. no. BNL-51134, 1979) p. 180. [5] E.A. Knapp, B.C. Knapp and J.M. Potter, Rev. Sci. Instr. 39 (1968) 979. [6] S.B. Hodge, L.W. Funk and S.O. Schriber, Proc. of the 1976 Proton Linear Accelerator Conference (Atomic Energy of Canada Limited- rep. no. AECL-5677, 1976) p. 344.

444

J.-P. Labrie, J. McKeown / Coaxial coupled linac structure

171 S.O. Schriber, E.A. Heighway and L.W. Funk, Proc. of the 1972 Proton Linac Conf. (Los Alamos Scientific Lab. rep. no. LA-5115, 1972) p. 140. [8] K.H. Halbach and R.F. Holsinger, Particle Accelerators 7 (1976) 213. [9] D.E. Nagle, E.A. Knapp and B.C. Knapp, Rev. Sci. Instr. 37 (i967) 1583. [10] P.B. Wilson and K.L.F. Bate, Stanford Linear Accelerator Center rep. PEP-226A (1977). I11] R.M. Sundelin, IEEE Trans. Nucl. Sci. NS-26 (1979) 3604. 112] M.A. Alien, L.G. Karvonen, J.-L. Pellegrin and P.B. Wilson, SLAC-PUB-1898 (March 1977). [13] J.N. Weaver, Stanford Linear Accelerator Center rep. PEP-342 (1981). [141 T. Weiland, CERN rep. no. CERN ISR-TH/80-24 (1980).

1151 K.C.D. Chan and J. McKeown, Proc. of 1981 I,inear accelerator conf. (Los Alamos Nat. Lab., 1981 ~. [16] J. McKeown, IEEE Trans. Nucl. Sci., NS-26 11979) 3423. [171 M. Sands and J. Rees, Stanford l.inear Ac~'eleratt~r Center rep. no. PEP-226A (1977). [18] J. McKeown, R.T.t,. Bird, K.C.D. Chan, S.It. Kidner and J.-P. Labrie, Proc. of 1981 Linear accelerator conf. (Los Alamos Nat. Lab., 198l). [ 19] A.F. tlarvey, "Microwave Engineering ~Academic Press, New York, 1963) p. 193. [20] J. McKeown, Proc. of Conf. on t:uture possibilities for electron accelerators University of Virginia, K-I (January 1979). [21] R.H. Helm and G.A. Loew, in Linear Acclerators, cds., P.M. Lapostolle and A.L. Septier (North-Holland, Amsterdam, 1970).