Silvestrov, G I

Skrinsky, A N

Vsevolozhskaya, T A

CERN Document Server

Particle Accelerators, 1990, Vol. 31, pp. 33-37Reprints available directly from the publisherPhotocopying permitted by license only© 1990 Gordon and Breach, Science Publishers, Inc.Printed in the United States of AmericaSUPERSTRONG QUADRUPOLES OF LIQUID METALFOR FINAL FOCUSING AT LINEAR COLLIDERESG.!. SILVESTROV, A.N. SKRINSKY and T.A. VSEVOLOZHSKAYAInstitute of Nuclear Physics, Novosibirsk, USSRTo solve the problem of linear collider fina'i focus, i. e.the problem of acceleratedbeams focusing to the interaction point into small size with beta-function value ofabout lcm " an extremely strong lens is to be used as the last focusing element. Besi-des the condition ~o~= F2 , which determines the lens focal distance F versus beta-func~tion values on the interaction point ~o and on the lens (3, an additional limitation to Farises in a form F·!1pjp<~o as a d~mand of small increase of interacting beam spotsizes due to particle energy spread I1pjp. The value of ~p/p i'n an accelerated beam isof the order of 1% " that for (3 0 = I cm leads to restriction F < 100 cm. If quadrupolesare considered for such a focusing their field gradient for a beam of I TeV energy is tobe of the order of 10 Tjmm or rnore. By that the ultilnate field available for forming byiron poles is exceeded already at a distancl' oj, 01 Illl11 from lens axis. With a smallvalue of beam emittance such an. aperture could he enough to, let pass the beam butshould not garantee the lens protection frOlTI the ra(Uation irom the interaction point.Besides a danger for lens saiety it would produce an extremely hard background con-ditions for a detector. Moreover d slll~t11 error in beal11 aliglll11ellt could result in thewhole beam caught by the lens bo(ty that should lead to all installt destroy of the lens.Looking more adequate to the problem is an iroldess quarupolc with comparati-vely large, of ---± 1 mm, aperture and high Inagnetic field, 'up to 1() T or more, at,theaperture periphery, fed with current pulses of short duralioll.\)otion «ironless» is con-sidered here as conditional only. Laminated iron could he used as it will be shownbelow for current conductors fixation and for back 11l;1~lletic ilu\ guiding but its parti-cipation in a field forming within the aperture is 1ll'g:ligihk due to the saturation athigh inductions.Field forming is fulfilled with current conductors only. Small size of a particlebeam reduces requirements to a forming accu racy bu t keeping its significance is a ratioof field gradient G to the maximum field value on the cOllductor surface Hmax restrictedby a possibility of metal destruction under field pressure. A'n increase of this ratio isone of the ways of conductor shape optimization including a rounding of angles and aproper choice of transverse sizes. Shown in' Fig. ,I is a ratio G/Hmax dependence ontransverse size of conductor cross section. By infiniteiy thin skin depth in conductorthis dependence occures to be the same for round conductor and for rectqngular withrounded angles (see Fig. 3). Maximum value of G j Hmax by that equals to 0.74 andtakes place by a conductor radious R equal to 0.55 of an aperture radious A. Finiteskin depth makes more flat the dependence of G j Hmax on R and slightly increases itsmaximum, up to 0.79 at 6=0.36A.Skin type of field distribution inside the conductor is resulted from small currentpulse duration necessary to reduce the Joule heating. Heat amount per pulse Q in thecase of thin skin depth 6«..R is proportional to b, i. e. depends on pulse duration as[1241]/3334/[1242]0.9G. I. SILVESTROV, A. N. SKRINSKY AND T. A. VSEVOLOZHSKAYAG/Hm4Xo 0;1 0.2. 0.3 0.4 0.5 0.6a,MHFIGURE 2. Joule heat Q per pulseand 1cm conductor length inround conductor of radious0.53 mm (1) and 0.75 mm (2) atfield gradient 10 TImm and aper-ture radious 1 mm versus skindepth.0.80.70.60.50.40, ~0.'2.0.1o '-.4 ~2 o.~ 0.11 0.5" O,E: 0.7 0.8 0.9RIA .FIGURE 1. Ratio GIHmax versus RIAfor round conductors with skin depthequal to: 1-0, 2-0-.09A, 3-0.36A.32.oQ, ~/cm.T1/ 2, while Q is proportional to T if 6~ R. Dependence of Q on R in round conductorremains lenear up to about 6=0.5 R (Fig. 2). By that the value of Q could be goodenough defined by an expression Q= l~ \ H2 ds (1), where the squared field integralover conductor surface is calculated in the infinitely th-in skin depth approximation.This expression might be as well applied to other geometries with the above correlationof 6 to a curvature radious of condu.ctor surface.Shape of conductor cross section is determined by the requirements of conductorfixation and of heat removal. Transfer from round conductor to rectangular with roundangles though results in current increase (Fig. 3) does not lead to a significant growthof Joule heat and in voltage. Value of voltage determines the minimum current pulseduration. At chosen lens parameters it is about 1 meso In copper conductor by that theskin depth is 0.09 mm and Joule heat is 0.22 J per I cmcondu.ctor length with the fieldgradient G = 10 Tlmm and aperture radious A = 1 mm. Thus at a repetition rate of100 Hz the heating power will be 22 W. With transverse -size of conductor cross sectionof "'"1 mm the heat -removal seems to be a very complicated problem. Its solution re-quires first of all the extention of conductor cross section in transverse direction so asin radial by change its shape into a triangular one (Fig. 4). This change results insome increase of Q value but it is the only way to dispose the cooling water channelsinside the conductor. It is particularly applied to a case where the back magnetic fluxis guided by a magnetic core so that ther.e are no restrictions for cross section exten-tion into a region where iron is not saturated. Such a quadrupole with field gradient oflOTImm and aperture radious of 0.5 mm having a complicated cooling system is nowunder development in CERN 3 For more aperture or maximum field value such typesystems do not look perspective.SUPERSTRONG QUADRUPOLES [1243]/35As a cardinal solution of cooling problem we consider the use of conductors ofliquid metal, pumped through with a high speed. Could be used for this purpose is analloy of gallium and indium having low melting temperature Tm= IB.5°C, or lithium(Tm= IB6°C) whose small density allows to have a high speed of metal pumping. Cer-tainly the change for conductors of liquid metal leads to an increase of Joule heatingdue to the speciHc resistance increase by 15 times as compared to copper conductor.However Q increase is not so large, by 4-5 times only, by benefit ·of skin type (thoughclose to violation with <5 =0.36 mm and r='0.5-0.75 mm) field distribution in conduc-tor.0.5oo 2 3" 5 , 1 8 9llA302010FIGURE 3. Joule heat (1) and current (2)dependence on the longitudinal size of crosssection in a rectangular conductor with roun-ded angles and equal to ± 0.53 of apertureradious the transverse cross section size.FIGURE 4. Cross section ofquadrupole. 1- titaniumenvelope, 2 -liquid metal,3-laminated iron, 4-cera-mic bars, 5-cylindric ban-dage.The main problem in working out the liquid metal quadrupoles consists in a pre-cise forming of surviving 400 bar pressure from 10 T field the current earring surfaceof liquid metal which determines the magnetic field forming accuracy. Principal designidea of such a quadrupole is clear from Fig. 4. Profile of liquid metal conductor isdetermined by a thin, of 0.1 mm, titanium or steinless steel envelope (1), leaned by itsmost part on surrounding laminated iron (3). Remained free is only a small part ofenvelope within the lens aperture. Laminated iron is simultaneously guiding the backmagnetic flux. In Fig. 4 the envelope is shown only schematically. In real structure itsthickness is small outside the iron and increases fluently along the surface of tangencyto it up to I mm on the opposite to aperture side of conductor. Envelope is brazed toiron along all surface of tangency. Four such laminated iron blocks with brazedconductors are precisely fixed by means of rectangular ceramic bars in cylindric ban-dage (5).With current pulse duration of 1 mcs the skin depth in titanium and steinlesssteel is 0.5 mm. Thus the free part of envelope outside iron is almost transparent for36/[1244] G. I. SILVESTROV, A. N. SKRINSKY AND T. A. VSEVOLOZHSKAYAmagnetic field and does not suffer from its pressure which is transmitted into liquidmetal. The mechanic loading of thin part of envelope will arise with a pressure pulsereflected from an opposite rigid envelope wall. Even if this reflected pulse amplitudewould be equal to an initial pressure pulse, i. e. to about 400 bar, the' tention in enve-lope material should be about 200 kgjcm2 only. That is several times less than the limitvalue and allows to hope that the ultimate magnetic field could considerably exceedlOT.As it was shown above with lOT jmm magnetic field gradient and 1 mcs currentpulse duration the full Joule energy per I cm conductor length is equal to about ---1 Jper pulse. Although the maximum temperature rise in the adjoining aperture part ofconductor will be 60°C, being averaged over whole conductor cross section (--20 mm 2 )it will be less than 3°C. With conductor lenght of 20 cm and speed of liquid metalpumping of 10 mjs the time of matter exchange in conductor will be 2 -I Oe- 2 s. Thuseven with a repetition rate of 1 kHz an average temperature will not exceed 60°C + Tm.Besides the solution of heat removal problem another cardinal advantage ofliquid metal lens consists in an absence of a problem of conductor surface destroyunder repeated thermal stresses which is the main restriction of magnetic field ampli-tude in solid conductors.Final focus quadrupole system will consist of a few independently fed elementsof about 20 cm length. Main restriction to element length is a reasonable voltage dropA-A.--~FIGURE 5. Longitudinal section of the lens with coaxial conic current input.Central cross section (5 - 5) is shown in schematic view: l-liquid metal con-ductor, 2-ceramic insulator.which can not exceed 10 kY. With 10 Tjmm field gradient and 1 mcs current pulseduration such a voltage corresponds to 20 cm length of element.Shown in Fig. 5 is the structure of one quadrupole element with coaxial coniccurrent input which serves' simultaneously for liquid metal supply. It feds four conduc-tors with current in series and with liquid metal in parallel. Such a supply of liquidmetal shortens by four times its way through the conductors with corresponding in-crease of the pumping speed. Conic shape of current input allows to insert coaxiallySUPERSTRONG QUADRUPOLES [1245]/37one element into another and to obtain a sequence of independently fed such quadru-pole elements.REFERENCES1. A.N. Skrinsky. Linear Colliders, Proc. XII Int. ConL on Hidh Energy Ace., Bata-via, 1983, p.104.V.E. Balakin, A.N. Skrinsky. VLEPP - Status Report, Proc. XIII Int. ConL onHigh. Energy Acc., Novosibirsk, 1986, v.l, p.IOI.2. K. Eqawa, T.M. Taylor. Conceptual Design of a 5 Tlmm Quadrupole for LinearCollider Final Focus, CERN LEP-MA/89-08 and CLIC Note 95.3. P. Sievers. Private communication.

Superstrong Quadrupoles Of Liquid Metal For Final Focusing At linear colliders

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