Crandall, K R

Ho, D D M

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Particle Accelerators, 1992, Vols. 37-38, pp. 105-109Reprints available directly from the publisherPhotocopying permitted by license only© 1992 Gordon and Breach Science Publishers, S.A.Printed in the United KingdomSCALING EXPERIMENT FOR HEAVY-IONFUSION FINAL FOCUSING*K. R. CRANDALLAccSys Technology, Inc., 1177A Quarry Lane, Pleasanton, CA. 94566D. D.-M. HOLawrence Livermore National Laboratory, Livermore, CA.(Received 3 December 1990)A scaling experiment will be performed to test the feasibility of proposed solutions to several problemsassociated with the final-focus system of heavy-ion driver for Inertial Confinement Fusion. The experimentwill be conducted at the Lawrence Berkeley Laboratory using a 120-keV Cs+ beam. The experiment willtest the proposed techniques for correcting geometric aberrations and for focusing variable-current beamsusing fixed strength quadrupoles.1 INTRODUCTIONIn a Heavy Ion Fusion (HIF) driver system, a high-current (several kiloamperes)beam of high-energy (several GeV) heavy ions must be focused to hit a small targetpellet (several mm in radius) in a short time interval (a few nanoseconds). To producethe proper compression of the pellet, the beam current deposited on the target mustvary in a prescribed manner over the pulse. Approximately 600/0 of the beamenergy should be delivered to the target during the final 20% of the pulse. Con-sequently, the final-focus system must be designed to focus a variable-current beamonto a fixed-radius target. A possible solution to this problem has been proposed.!After the heavy-ion beam has been accel'erated to its final energy, it is longitudinallycompressed to the desired pulse length as it is transported to the final-focus systemthrough a periodic array of quadrupole magnets. The final-focus system consists of:1) a drift space of several meters which allows the beam to expand transversely; 2)several large-aperture quadrupole magnets to focus the beam onto the target; and3) a drift space of several meters through the reaction chamber to the target. Thefringe fields of the large-aperture quadrupoles can produce third-order geometricaberrations that distort the beam in transverse phase space. An energy spread in thebeam can cause chromatic aberrations. Unless they are eliminated or corrected, theseaberrations, together with nonlinear space-charge forces, can cause a significant* This work is supported by the U.S. Department of Energy under Small Business Innovative Researchgrant # DE-FG03-90ER81076.105106 K. R. CRANDALL AND D. D.-M. HOfraction of the beam to miss the target pellet. Several proposals2 ,3,4,5 have been madefor using octupoles to correct the third-order geometric aberrations.Although it is not practical to study the abovementioned problems and theirpossible solutions in a full-scale experiment, a scaled-down experiment can demon-strate some of the same problems and test the feasibility of some of the proposedsolutions. In the early 1980s, a Single Beam Transport Experiment (SBTE) wasconducted at Lawrence Berkeley Laboratory (LBL) to study emittance growth inspace-charge-dominated beams being transported through a periodic focusing chan-nel. 6 In the SBTE, a 120-keV Cs + beam was transported through a periodic arrayof 82 electrostatic quadrupoles. The scaling experiment discussed here calls for theSBTE apparatus to be recommissioned and for the downstream portion of thequadrupole array to be replaced by four large-aperture quadrupoles. The mainpurposes of the scaling experiment are: 1) to demonstrate that the beam size at thetarget can be kept relatively constant as the current is varied by a factor of three orfour; 2) to show that the geometric aberrations can be corrected by using octupoles;and 3) to study the effects of chromatic aberrations on the beam size at the target.2 FOCUSING A VARIABLE-CURRENT, CONSTANT-EMITTANCE BEAMTheoretical studies and numerical simulations7 both indicate that the transverseemittance of the beam remains relatively constant as the beam is being compressedlongitudinally. At the entrance of the final-focus system, the transverse emittanceshould therefore be constant along the beam pulse, even though the current varies.Also, if the beam is matched to the transport system at the beginning of thelongitudinal compression, it should remain matched throughout the transport systemand at the input of the final focus. Because of the high currents required for HIF,the beam will undoubtedly be space-charge-dominated in the final-focus region,which means that the beam size will be proportional to the square root of the current.If this condition also applies near the target, then the final focusing quadrupolesshould be adjusted to produce the desired spot size for the highest current in thepulse. The lower-current portions of the pulse will produce a smaller spot size at thetarget.However, because of the small size of the target, the beam may not be space-charge-dominated near the target. The envelope equation for a circular beam in adrift space is:" q2J E2r - --=02TCeomc3(f3y)3 r r3 'where r is the outer radius of the beam, q is the charge state, J is the particle current,eo is the permittivity of free space, m is the mass of the heavy ions, c is the velocityof light, f3 and yare the standard relativistic parameters, and E is the totalunnormalized emittance (4 times the rms emittance). The prime denotes differentia-tions with respect to the longitudinal coordinate. The second and third terms in theHIF FINAL FOCUSING 107above equation are the space-charge and emittance terms, respectively. As the beamsize decreases, the emittance term increases much faster than the space-charge term.We have found that, as long as the space-charge term is not much lower than halfof the emittance term at the target, the final-focus quadrupoles can be set to producean almost constant beam size as the current is varied by a factor of 3 or 4. 1 Additionalrequirements are that the beam must be space-charge-dominated at the entrance tothe final-focus system and the beam must be axisymmetric at the beginning of theexpansion drift space.3 CORRECTING THIRD-ORDER ABERRATIONS WITH OCTUPOLESThird-order aberrations, produced mainly in the fringe fields of the large-aperturequadrupoles, can distort the beam in phase space and cause a significant fraction ofthe beam to be outside of the target radius. Octupole magnets, which also exertthird-order forces on a charged-particle beam, can theoretically be used to cancelthe third-order quadrupole aberrations. For this technique to be successful, both thequadrupole aberrations and the octupole corrections must not be large enough tosignificantly perturb the first-order dynamics in the vicinity of the quadrupoles.There are three major third-order aberration terms produced by the quadrupolefringe field and therefore a minimum of three octupoles are required for theircorrection. More than three octupoles should be used so that the correction termscan be relatively small. The octupoles give the best results when they are placedwhere the beam is the largest, which implies that some octupoles should besuperimposed on quadrupoles. Others could be placed between quadrupoles.4 SCALING EXPERIMENTThe results of the SBTE reported in reference 6 indicate that the beam current andemittance are in acceptable ranges to be useful for testing the validity of the proposedsolutions to some HIF final-focus problems. Up to 15 rnA of 120-keV Cs+ ions weretransported through the electrostatic quadrupole array and the nleasured normalizedemittance was about O.ln mm-mrad (70n mm-mrad, unnormalized) when the zero-current phase advance was set at 59° per period. The space-charge and emittanceterms in the envelope equation are equal whenI = 0.0057 £2/r2,where I is the current in rnA, r is the beam radius in mm, and £ is the emittance inn mm-mrad. Choosing an emittance of 60n mm-mrad and a target radius of 2.5 mmgives a value of 3.3 rnA for the current at which the space-charge and emittance termsare equal. A suitable current range for the experiment would then be from 2 to 8 rnA,for example. The current would be adjusted without changing the emittance byusing various filters. The emittance and the current could both be reduced by a seriesof apertures.P.A.-E108 K. R. CRANDALL AND D. D.-M. HOThe first step in the experiment is to recommission the SBTE apparatus, whichconsists of vacuum enclosures with pumps; a Cs + ion source and high-voltage powersupply; 5 electrostatic quadrupoles for matching the beam from the ion source tothe periodic quadrupole array; several periods of an electrostatic quadrupole lattice;sever·al types of diagnostic hardware; and an automated data acquisition system. Afterrecommissioning this apparatus, the beam will be characterized as to its emittanceand current range. A special electrostatic quadrupole may need to be added to theend of the periodic array so that the beam can be made axisymmetric at this point.The preliminary design of the final-focus system calls for a 45-cm expansion driftto be followed by four magnetic quadrupoles. (Electrostatic quadrupoles wereintended to be used, but these cause much larger aberrations because of the energyvariation produced in the beam as it passes through these elements.) The two innerquads would have effective lengths of about 25 em and the two outer quadswould have effective lengths of 15 cm. There would be 20 cm between quadrupolesand 10 cm from the end of the last quad to the target. An 8-mA beam with anemittance of 60n mm-mrad would have a maximum radius of about 65 ·mm in theinner quads, so these quads would need a relatively large aperture. Furthermore,these two quads would have octupole elements superimposed. The outer two quadscould have smaller apertures, perhaps half as large as the inner two. Short octupolescould be placed between the quads. The magnetic fields at the pole tip of thesequadrupoles would be on the order of 10 kilogauss. The pole tip field required forthe octupoles could be 1 or 2 kilogauss.After characterizing the beam, the next step would be to find a focusing solutionfor the highest current to be used. This will probably not be trivial because thethird-order aberrations will complicate matters. It is difficult enough to find atheoretical solution in a computer simulation in which the third-order effectscan be turned on or off. It will be much more challenging to find a solutionexperimentally.Most of the experimental measurements will be made using the central part of thefew microsecond pulse, in which the beam is essentially monoenergetic. Space-chargeforces will cause an energy deviation in the beam at each end of the pulse. The effectsof chromatic aberrations in the final-focus system can be studied by observing thespot sizes at the ends of the pulse.At this writing, the scaling experiment is still in the design phase. i\. search is beingmade for suitable large-aperture quadrupoles. If these cannot be found for areasonable cost, the experiment will have to be modified. The emittance and thecurrent could both be reduced to allow the final-focus quadrupoles to have smallapertures. The variable-current focusing could still be tested, but the third-orderaberrations might be relatively insignificant, which would negate one of the purposesof the experiment.REFERENCES1. K. R. Crandall, Final Report to U.S. Department of Energy, contract # DE-AC03-89ER80768, April1990.HIF FINAL FOCUSING 1092. D. Neuffer, Proe. of the HIF Workshop, ANL-79-41, pp. 333-339 (1978).3. S. Fenster, ibid., pp. 355-364.4. E. P. Colton, ibid., pp. 365-378.5. D. D.-M. Ho, I. Haber, K. Crandall and S. Brandon, Proe. 1989 Part. Aeeel. Conf., IEEE publication89CH2669-0.6. M. G. Tiefenbaek, PRo D. thesis LBL-22465 (1986).7. D. D.-M. Ho, S. T. Brandon and E. P. Lee, Part. Accel. (to be published).

Scaling experiment for heavy-ion fusion final focusing

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