Ng, K Y

Qian, Z B

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FINEMET VERSUS FERRITE — PROS AND CONSK.Y. Ng and Z.B. Qian, FNAL∗, Batavia, IL 60510AbstractThere is a new magnetic alloy called Finemet which hasvery constant 0pQf up to 2 kG and is very stable at highmagnet flux density and temperature. It may be a good can-didate for high-gradient rf cavities.However, it has a ratherlow quality factor and is therefore very lossy. We comparethe pros and cons of Finemet versus the common ferrite,when used in low-energy accelerating cavities, insertion forspace-charge compensation, and barrier cavities.1 INTRODUCTIONFerrite has been used extensively in rf cavities for particleaccelerators that require tuning. Some ferrite used can op-erate up to more than 100 MHz but the saturation magneticflux intensity is often limited to 100200 G. Recently, thereis a met-glass-like material called Finemet developed inJapan [1] that can hold up to 2 kG of magnetic flux intensity(Fig. 1). Ferrite is ceramic in nature and is manufactured bybaking in an oven. Therefore, large ferrite cores are diffi-cult to produce. On the other hand, Finemet is in the formof a tape which can be wound into a core over 1 m in diam-eter, making very high magnetic flux possible. For this rea-son, Finemet may open up a new way to the construction ofhigh gradient acceleration cavities. However, there are alsoshortcomings. Its relative permeability 0p starts to drop ata much lower frequency, 2 MHz, and the quality factor islow, Q1, although they can be boosted to 8 MHz andQ12 by cutting the cores and leaving an air gap betweenthe two semicircular halves. This implies that Finemet ismore lossy with larger power consumption. Fortunately,Finemet has a Curie temperature600C while that for fer-rite is only 100 to 200C, meaning that heat dissipation willbe more efficient. The manageable power dissipation [1]is believed to be around 10 W/cm3. Thus, the limitationsFinemet are power dissipation and high frequency, whilethat of ferrite is high magnetic flux density, In this note, wecompare the use of Finemet and ferrite in three respects: ac-celerating cavities, space-charge compensating insertions,and rf barriers for multiple-turn injection. The proposed fu-∗Operated by the Universities Research Association, under contractwith the US Department of Energy.Figure 1: Plots showing the 0pQf properties of ferrite andFinemet as a function of magnetic flux density.ture Fermilab low-energy booster and the Brookhaven AGSwill be used in the application.2 ACCELERATING CAVITIESThe future Fermilab booster consists of two rings [2]. Thelow-energy ring has a circumference of 158.0676 m (1/3 ofpresent booster), cycles at 15 Hz, and accelerates 4 protonbunches, Nb = 2:5 1013 protons each, from kinetic en-ergy 1 GeV to 3 GeV. The 10 accelerating cavities have arf frequency span of 6.638 to 7.368 MHz, and require a to-tal peak voltage of  190 kV, or  20 kV each. For such asmall ring, small cavities are preferred, making high-fieldFinemet very appealing. The FT3M Finemet cores consid-ered here have inner and outer radii 10 and 50 cm, respec-tively, while the Philips 4M2 ferrite cores have inner andouter radii 10 and 25 cm. Both cores have a thickness of2.54 cm. The Finemet cores are cut with an air separation of4.6 cm so that the quality factor can be boosted to Q=11:4[1]. The details are listed in Table 1. If there were only onecore, the flux density would be Brf =Vrf=(!rfAf ). To limitdissipation to below the manageable 10 W/cm3, at least 2Finemet cores are required per cavity. Allowing2:54 cmseparation between cores for air cooling, the lengthof a cav-ity can be made as short as  13 cm. However, the powerloss is 324 kW per cavity. On the other hand, if ferrite isused, to satisfy its flux density limitation, we need 11 coreswith a total cavity length28 cm. Here core spacing is notrequired because the total power loss for the whole cavityis only 10:2kW. Although longitudinal space is saved in theFinemet cavities, power loss will be 31.8 times larger, total-ing 3.24 MW for 10 cavities. Assuming the acceleration of11014 particles takes place in 1/30 of a second, the averageTable 1: Properties of a Finemet and a ferrite cavity.Finemet FerriteInner radius ri 10.00 10.00 cmOuter radius ro 50.00 25.00 cmCore width t 2.54 2.54 cmFlux area Af = (ro−ri)t 101.60 38.1 cm2Core volume Vc = (r2o−r2i )t 19155 4189 cm3Rf frequency frf 7.37 7.37 MHzQuality factor Q 11.4 450pQf at frf 6.00 61.0 GHzPermeability (Re) 0p 71.43 184.0Permeability (Im) 00p = Q0p 814.33 8279Inductance L 0.5840 0.8654 HResistance R = Q!rfL 308.2 1784 ΩCapacitance C = 1=(!2rfL) 798.9 544.9 pFAccelerating voltage Vrf 20 20 kVTotal flux density if one core Brf 425.2 1134 GSuitable flux density per core 250 100 GNumber of cores required N 2 11Power per core P1 162.2 0.926 kWPower for N cores P = NP1 324.4 10.19 kWPower per volume P1=Vc 8.47 0.221 W/cm30-7803-5573-3/99/$10.00@1999 IEEE. 872Proceedings of the 1999 Particle Accelerator Conference, New York, 1999power delivered to the particles is only 0.96 MW. Of course,more Finemet cores can be used to reduce the power dissi-pation, but its advantage of accommodating high flux den-sity will be lost. However, Finemet cavities do have othermerits. Because of the low quality factor, no tuning may benecessary during the whole acceleration cycle, and the cav-ity may be able to encompass several higher harmonics. Infact, a multiple-harmonic cavity had been built using simi-lar material but in amorphous form called Vitrovac [4].Each bunch carries a charge of q=4:0 C. On passage ofa cavity, some amount of negative charge will be depositedat the upstream end of the gap. An equal amount of posi-tive charge will accumulate at the downstream end. For aGaussian bunch, the transient beam-loading gap voltage ata time t after the bunch center passes the cavity gap isVt =q!rR2Q cosRe ejφ−t2/(2σ2τ)w[τ!rejφp2− jtp2τ]; (1)where w is the complex error function, sin=1=(2Q), Rthe total resistance of all the cores in series. When the rmsbunch length τ!0, this becomes q=C , C being the totalcapacitance of all the cores in series. With τ = 12:63 ns,Vt reaches the maxima of 5.30 and 44.6 kV, respectively,for the Finemet and ferrite cavities when t0:85τ . This isunderstandable because there are many more ferrite coresthan Finemet cores in a cavity. Since Vt are not negligi-ble with respect to the designed gap voltage, compensationsmust be made at the gap through feed-forward [3]. If theFinemet cores do not have the 4.6 cm gap, one will have0pQf = 3:7 GHz and Q = 1 instead. Now 3 cores have tobe used. The power dissipation increases to only 351 kW,but the maximum beam-loading voltage to 34.8 kV.The inductance of Finemet is very sensitive to the longi-tudinal bias field, as is illustrated in Fig. 2. This is a merit inthe sense that the inductance can be changed easily. How-ever, this can also be a disadvantage that the precision ofinductance control will be much worse than ferrite.3 SPACE-CHARGE COMPENSATIONA high-intensity and low-energy bunch experiences a largelongitudinal space-charge force. A particle at time advance from the bunch center sees, for each turn, a space-chargevoltage Vspch = −!−10 (d=d)jZk=njspch, where () isthe linear density of the bunch and !0 the angular frequencyof the ring. The space-charge impedance per harmonic isZk=n = −jZ0[1+2 ln(b=a)]=(2γ2), where  and γ arethe Lorentz factors, Z0  377 Ω, a and b the radii of thebeam and the beam pipe. In order to keep the beam parti-cles bunched, extra rf voltage will be required. One wayto cancel this space-charge impedance is to add an induc-tive insertion in the vacuum chamber [5]. Such an attempt[6] had been performed at the Los Alamos PSR, where 60Toshiba M4C21A ferrite cores were inserted intending tocancel about 2/3 of the space-charge force. Wire windingson the outside were used to provide perpendicular biasingso that the relative permeability of the ferrite could be con-trolled. With the ferrite insertion, it was found that onlyabout 2/3 of the usual rf voltage would be required to keepFigure 2: Sensitivity to bias field for Finemet and ferrite.the bunch stable. When the solenoidal current was turnedon, the bunch was found lengthened. Thus the ferrite inser-tion did actually cancel part of the space-charge force. An-other similar experiment had been performed at the KEKProton Synchrotron with 8 Finemet cores [7]. The incoher-ent quadrupole synchrotron frequency was measured as afunction of beam intensity. The slope of the frequency wasreduced by half. The result is consistent with a partial can-cellation of the space-charge impedance.Here, we would like to apply the inductor insertion to theFermilab low-energy booster ring, with bunches having halfwidths ^ =p5τ =28:25 ns. The space-charge impedanceper harmonic is about −j89:5 Ω. Unlike the acceleratingcavities, the bunch current will dump energy into the inser-tion at all frequencies. To estimate this energy, assume asimple model consisting of an ideal inductance L and anideal resistor R in parallel, which givesZ(!)=j!L1 − j!=!r1 + !2=!2r/ j!(0s−j00s ) ; !r =RL; (2)so that the series 0s is relatively constant at low frequen-cies and rolls off near !r , while 00s increases as ! at lowfrequencies and resonates at !r. The corresponding longi-tudinal wake potential is W (t) =R [ (t)−!re−ωrt ] ; andthe energy the particle lost to the inductor in one passage isE = 3e2Nb2[!^3+1!r!0] ∣∣∣∣Zkn∣∣∣∣ind; (3)where a parabolic bunch distribution has been assumed.The first term is the linear force from the inductive impe-dance Zk=njind = j!0L, which is supposed to cancel thespace-charge force, leaving behind the second term, whichis the actual energy lost to the insertion. Thus for nb = 4bunches the total power lost to the insertion becomesP =3enbN2b4!r ^3∣∣∣∣Zkn∣∣∣∣ind: (4)If ferrite having a resonant frequency !r=(2)=60 MHz isused, the power lost to the insertion amounts to 0.16 MW.Assuming the ferrite cores in Table I,  34 cores will berequired for space-charge cancellation. On the other hand,if Finemet having a resonant frequency 6 MHz is used, theloss becomes 1.6 MW. According to Table 1, 15 Finemetcores are required. The heat dissipation will be 5.6 W/cm3.However, not much longitudinal space is gained by usingFinemet but much more energy has to be injected to coun-teract the power loss. If uncut Finemet core with Q = 1873Proceedings of the 1999 Particle Accelerator Conference, New York, 1999is used, the resonant frequency is 1 MHz and the powerloss will be increased 6-fold. Here, the merits of high 0pfor Finemet can hardly be utilized, because that will lead toa lower Q and lower !r , thus increasing the power loss.Using the same calculation, the power loss to the ferritecores in the Los Alamos experiment is only 0.82 kW evenwhen the resonant frequency is only 30 MHz. This is be-cause the power loss is inversely proportional to the cubicpower of the bunch length. At the Los Alamos PSR, the halfbunch length was ^133:6 ns, which is 4.73 times longer.Also, there were only 2:51013 particles in the PSR.4 RF BARRIERSRf barriers are designed in the Fermilab Recycler ring toconfine the antiprotonbeam bunch and shape the bunch dis-tribution waiting for the next collider refill. Rf barriers arealso planned to be used in the Brookhaven AGS and theJapan Hadron Project for multiple injections. For the lat-ter, tens of kV are required and a barrier cavity is neces-sary. We model the cavity by a parallel RLC circuit. Whenthe switch is closed, the current generator delivers a currentI(t) = I0(t). The cavity gap will respond with a voltageV (t) = (t)I0RQe−αt sin !t ; (5)where !r = (LC)−1/2 is the angular resonant frequency, =!r=(2Q), ! =√!2r−2, and Q =R=(!rL) the qual-ity factor. If the current is turned off at t=2=!, or anothercurrent pulse of opposite sign is turned on at that time, thecavity gap voltage will vanish due to cancellation, provid-ing that the degradation exp(−2=√4Q2−1) is not too ex-cessive. A cycle of sinusoidal gap voltage is generated withpeak voltage V0  I0R=Q. Thus, a large Q will require alarge current pulse. But a small Q will lead to incompletecancellation of the sinusoidal rf wave after the current pulse.Consider a rf barrier at barrier frequency fb =!b=(2)=2 MHz and barrier voltage Vb =40 kV in the AGS. This im-plies a barrier length of 0:5 s, while the AGS circumfer-ence at 1.5 GeV injection kinetic energy is 2:917 s. Againwe use the large FT3M Finemet cores with a cut of 4.6 cmand the 4M2 ferrite listed in Table 1. The properties of sucha Finemet or ferrite barrier cavity are listed in Table 2. Inorder to keep the power loss of Finemet below 10 W/cm3,we have to use at least 6 cores with an average flux den-sity of 522 G. If ferrite is used, the average flux density hasto be limited to 100 G, requiring 84 cores. The Finemetcavity will take up only  33 cm while the ferrite cavity214 cm. However, the power dissipation in the Finemet is95.6 times larger than the ferrite. Since the barrier wave isonly present for 0.5 s, the average power dissipation Pavis about 148 kW for the Finemet and 1.55 kW for the fer-rite, much less than those computed in the rf cavities in Sec-tion 1. Finemet may therefore be a good choice in buildinga barrier cavity if space limitation is a serious problem.For an AGS bunch with 6:01012 protons and τ =60 ns,the transient beam-loading voltages computed using Eq. (1)have maxima 0.20 and 4.5 kV, respectively, for the FinemetTable 2: Properties of a Finemet and a ferrite barrier cavity.Finemet FerriteBarrier frequency fb 2.00 2.00 MHzQuality factor Q 24 1100pQf at fb =2 MHZ 3.00 36.0 GHzPermeability (Re) 0p 62.5 163Permeability (Im) 00p = Q0p 1500 18000Inductance L 0.511 0.762 HResistance R = Q!bL 154 1053 ΩCapacitance C = 1=(!2bL) 12400 8314 pFBarrier voltage Vb 40 40 kVTotal flux density if one core Brf 3133 8355 GSuitable flux density per core 522 100 GNumber of cores required N 6 84Peak power per core P1 144.2 0.1077 kWPk power for N cores P = NP1 865.2 9.046 kWAverage power for N cores Pav 148.3 1.55 kWAv power per volume Pav=(NVc) 7.53 0.026 W/cm3and ferrite barrier cavities. If required, they should be com-pensated by feed-forward. If uncut Finemet cores are used,0pQf =2 GHz and Q=1. One requires 7 cores so that theloss is still below 10 W/cm3. The total average power dissi-pation increases to only 191 kW, but the maximum transientbeam-loading voltage jumps to 2.2 kV.5 CONCLUSIONIt is clear that longitudinal space will be saved and transientbeam loading will be smaller when Finemet is used insteadof ferrite, especially in acceleration and barrier cavities.However, this gain arrives at the expense of much largerpower dissipations. The obvious reason comes from thefact the Finemet has much lower resonant frequencies andlower Q’s than ferrite. Therefore when longitudinalspace islimited, especially for very small low-energy rings, Finemetcavities may be a solution. It is possible that Finemet willbecome very valuable in other applications at sub-MHz fre-quencies when high magnetic flux densities are required.The authors wish to thank Dr. J. Griffin for discussions.6 REFERENCES[1] Y. Mori, KEK Tanashi, private communication. Y. Tanabe,“Evaluation of Magnetic Alloy(MA)s for JHF rf Cavity”, talkgiven at Mini Workshop, Tanashi, Japan, Feb. 23-25, 1998.[2] C. Ankenbrandt, private communication.[3] J.E. Griffin, “RF System Considerations for a Muon ColliderProton Driver Synchrotrons”, Fermilab report FN-669, 1998.[4] P. Ausset, G. Charruau. F.J. Etzkorn, C. Fougeron, H. Meuth,S. Papureanu, and A. Schnase, “A High-Power Multiple-Harmonic Acceleration System for Proton- and Heavy-IonSynchrotrons”, PAC 95, May 1-5, 1995, Dallas, p.1781.[5] A.M. Sessler and V.G. Vaccaro, “Passive Compensation ofLongitudinal Space Charge Effects in Circular Accelerators:the Helical Insert”, CERN, ISR Div. 68-1, 1968.[6] J.E. Griffin, K.Y. Ng, Z.B. Qian, and D. Wildman, “Experi-mental Study of Passive Compensation of Space Charge Po-tential Well Distortion at the Los Alamos National LaboratoryProton Storage Ring”, Fermilab FN-661, 1998.[7] K. Koba, S. Machida, and Y. Mori, KEK Note, 1997.874Proceedings of the 1999 Particle Accelerator Conference, New York, 1999

Finemet versus ferrite: Pros and cons

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