ࡱ> Root Entry۶mmmm۶mmmm۶mmmm۶m FmmmۀRԽ.'mmDatamm۶mmmm۶mmmm۶mmmm۶mmmm mmm۶mmmm۶mmmm۶m"}mWordDocumentmm۶mmmm۶mmmm۶mmmmmmm۶mmmm۶mmmm۫|VmObjectPool۶mmmm۶mmmm۶mmmm۶m >xԽUyԽm۶mmm - !*#$%&'()>+,3q/0249578:=;y?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmt|z}1TablegSummaryInformation(TDocumentSummaryInformation8[CompObj X16<Root Entry۶mmmm۶mmmm۶mmmm۶m FmmmԽ.'mmDatamm۶mmmm۶mmmm۶mmmm۶mmmm mmm۶mmmm۶mmmm۶m"}mWordDocumentmm۶mmmm۶mmmm۶mmmmmmm۶mmmm۶mmmmەRmObjectPool۶mmmm۶mmmm۶mmmm۶m >xԽUyԽm۶mmm  !*#$%&'()>+,3/0249578:=;y?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmoprsuvwx~z0Tabler_966070208)#F}&Խ}&ԽOle PIC "%L16{<es acting on the liquid layer. The code can also model macroscopic erosion of a solid target from brittle destruction due to thermal stresses. We can easily implement models to study wall erosion from the impact of energetic liquid-droplets. (2) Liquid jet dynamics in a strong nonhomogeneous field Liquid material conductivity is not small therefore, the magnetic field diffusion-time  EMBED Equation.2 is comparable with the flight time (v . Due to the force  EMBED Equation.2  the jet trajectory becomes concave. To calculate such trajectory in order to choose better conditions for energy deposition and pion production, detail MHD analysis is necessary of the jet dynamics in a nonhonogeneous magnetic field (near the end of coils). This problem can also be studied with the A*THERMAL-S code including all components of the electromagnetic forces, but may require some modifications of the code. (3) Liquid-jet stability Because of the existence of a radial component of the jet velocity the magnetic field will be distorted. The magnitude of the magnetic field will be less on back side of the cylindrical column than on the front side. This could result in a liquid metal flow from the front side to the back one therefore, the shape of the jet could changes from circular form to an elliptical one. Decreasing the value of the magnetic field from coil inner surface to axis z can stabilize this instability. The treatment of this problem can be made analytically using convential MHD stability theory. (4) Inlet/outlet problem One other problem is how to inject a free surface liquid jet into a nonhomogeneous magnetic field. It is known that during jet injection, the hydrodynamic instability due to capillary forces takes place with the increment:  EMBED Equation.2  with ( is the surface tension. The time of this instability (((10/( is about few ms which is comparable or less than the flight time (v. Therefore the arising of this well known instability can result in dividing of the liquid jet into droplets with size about 0.1R (R being the jet radius). Of course this is not desired from the efficiency of pion production point of view, another problem is how to collect these droplets in the outlet system. This problem can be modeled analytically using conventional MHD theory and experimental data of time of droplet formation and droplets size. (5) Energy deposition experiments It may be possible to simulate the beam-on-target energy deposition and resulting target breakup using exploding wire technology. Such experiments could potentially be much less expensive than true beam-on-target tests. We propose to evaluate the extent to which exploding wires in liquid metals could provide useful, target-relevant information and set up a simple test stand to obtain some first results. Our computer modeling capability will be used to guide the testing, interpret the results, and evaluate the relevancy to actual beam-on-target tests. Initial testing would be done in a static or slowly-flowing liquid metal and without a magnetic field. 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B@Rܠ"yI{y T@Rܠ"y{!QU]_X\`4?Hhl"z56NOP@QBQ@QBQ@QBQD@QBQBQBQBP@QDQ*@QDQZ@QDQ@QXDQ @Q\DQ|!@QrDQ!@Q~DP!@QFQFQh"@Q FQ"@QFQFQD#@QFPFQF#@Q#@QFQ#@P.FQ#@Q0FP#@Q#@Q2FQn$@Q:FQ$@QBFQ%@QJFQ%@QLFQ%@QTFQ<&@Q^FP&@PRP<'@QtFP\'@QHQ(@Q@HQFHQD)@QHHQ)@QLQ)@Q$*@Q"LQ.*@Q&LQ+@Q,LQn+@QxԽ>xԽOle PIC LMETA _960012782!F>xԽ>xԽOle  PIC  !LMETA #es"qhR(&5(&,(&M -#>0(BbD(1) Jet Heating and ExpansionAHAH]2ZV :(******,vjlVVAH H Muon Target/AH+KM/FAHn31nMicrosoft Word 8.0@l/V@0rս@O(Խ@O1սMp ՜.+,D՜.+,H hp|  'ALe- (: (1) Jet Heating and Expansion Title 6> _PID_GUID'AN{AE57B181-3DC5-11D2-BF94-A0FB5F4D9D16}N0LO t s =R e2 D,whereD=c e  e2 4ps5CJ 2B`2 Body Text $ hFMicrosoft Equation Editor 2.0uation Equation.29q| |tm||<n||XoO<lJqJlJ g=  2srR  |t|sO|t Oh+'0  4 @ L Xdlt|'(1) Jet Heating and ExpansionMi1) the small Tred from the efficiency of pion-in addition, also the c }jbjbSS R11L]2Z :,l>> ZR @V@ ~ N PZ 6> _PID_GUID'AN{AE57B181-3DC5-11D2-BF94-A0FB5F4D9D16}N0LO t s =R e2 D,whereD=c e  e2 4ps5CJ 2B`2 Body Text $ hFMicrosoft Equation Editor 2.0uation Equation.29q| |tm||<n||XoO<lJqJlJ g=  2srR  |t|sO|t Oh+'0  4 @ L Xdlt|'(1) Jet Heating and ExpansionMi1)  MODELLING OF BEAM-TARGET INTERACTION IN THE MUON COLLIDER DEVICE (Ahmed Hassanein and Kirk McDonald) Introduction The problems associated with proton beam deposition in the liquid target of the Muon collider are not fully resolved to assure reliable and steady successful operation. The resulting effects of the beam heating of the target can cause the destruction of the solid or liquid target, reduction in pion production, and possible damage to the magnet system Some of the concerns are associat_960012780F>xԽ>xԽOle :PIC ;LMETA =ed with the motion of liquid-metal jet in a strong and nonhomogeneous magnetic field, the hydrodynamic instability of the liquid jet, thermal stresses, and the shock wave effects resulting from the sudden deposition of the proton energy in the liquid target. In this work we propose to use our comprehensive numerical simulation package to study the various effects of sudden heat deposition in the liquid jet. A brief summary of the actual concerns associated with the Muon collider target is described below, as well as a brief description of the proposed work to these effects. (1) Jet Heating and Expansion Detail simulation of the dynamics of a cylindrical column of radius Rm of the liquid metal either with a free surface or confined by the solid cylinder is proposed. The transport equations of continuity, motion, and heat balance are solved in a strong magnetic field, using the particle-in-cell (PIC) method in cylindrical coordinates (r, z) assuming symmetry along azimuthal angle (. The problem of stability as a function of the angle ( will be solved separately. Because the deposited energy Qbeam depends on r and z it is necessary to regard the media motion in two directions r and z. The existance of a free surface requires the use of Lagrangean description for the numerical mesh of the target. However, to avoid the problem of large distortion of the hydrodynamic cells it is necessary to use mixed Eulerian-Lagrangean scheme. The more adequate description is achieved using the 2-D PIC method recently implemented in the A*THERMAL-S code. This code is a part of the HEIGHTS package to study High Energy Interaction with General Hetrogeneous Target System. The 2-D PIC method is most suitable for studying the dynamics of a target with free surface as well as of the resulting shock wave propagation that might be generated during the intense energy deposition. The results from the computer simulation will show whether a pressure wave is generated inside the liquid jet and in addition study the consequences of such shock wave on jet behavior. The magnitude of the pressure wave will determine the severity of jet breakup and distortion. In the case that a strong pressure wave is generated inside the jet and, as a result, the jet is broken into energetic droplets flying inside the magnet, the SPLASH code can then be used to study the droplet impacts on the chamber wall. The current SPLASH code models the hydrodynamic stability and splashing effects of a free-surface liquid metal layer subject to various forcxF0F$h$ h$/ =!"#$%|HH(FG(HH(d'`,, and stability and its propagation/reflection of thatshing effects of a free-surface of a isimpact and ingingthe The letal, Because of , andthe bothsthe usinghowever, it(3) Liquid-jet etic field will be less on back may side to the back one therefore,FHLvNxNzNNP j7yEHUj!9 CJOJQJUVmHthis could alter a mayanalysisthe onfree surface liquid jet into a Another problem is nonhomogeneous magnetic field. can take,where,, development0FR$|HH(FG(HH(d'`,, and stability and its propagation/reflection c jbjbSS |V11O]$z B :| | | | | | | ,l| | | | |  | | R   | | | @V@|  ~  z*v  MODELLING OF BEAM-TARGET INTERACTION IN THE MUON COLLIDER DEVICE (Ahmed Hassanein and Kirk McDonald) Introduction The problems associated with proton beam deposition in the liquid target of the Muon collider are not fully resolved to assure reliable and steady successful operation. The resulting effects of the beam heating of the target can cause the destruction of the solid or liquid target, reduction in pion production, and possible damage to the magnet system Some of the concerns are associated with the motion of liquid-metal jet in a strong and nonhomogeneous magnetic field, the hydrodynamic instability of the liquid jet, thermal stresses, and the shock wave effects resulting from the sudden deposition of the proton energy in the liquid target. In this work we propose to use our comprehensive numerical simulation package to study the various effects of sudden heat deposition in the liquid jet. A brief summary of the actual concerns associated with the Muon collider target is described below, as well as a brief description of the proposed work to these effects. (1) Jet Heating and Expansion Detail simulation of the dynamics of a cylindrical column of radius Rm of the liquid metal either with a free surface or confined by the solid cylinder is proposed. The transport equations of continuity, motion, and heat balance are solved in a strong magnetic field, using the particle-in-cell (PIC) method in cylindrical coordinates (r, z) assuming symmetry along azimuthal angle (. The problem of stability as a function of the angle ( will be solved separately. Because the deposited energy Qbeam depends on r and z it is necessary to regard the media motion in two directions r and z. The existance of a free surface requires the use of Lagrangean description for the numerical mesh of the target. However, to avoid the problem of large distortion of the hydrodynamic cells it is necessary to use mixed Eulerian-Lagrangean scheme. The more adequate description is achieved using the 2-D PIC method recently implemented in the A*THERMAL-S code. This code is a part of the HEIGHTS package to study High Energy Interaction with General Hetrogeneous Target System. The 2-D PIC method is most suitable for studying the dynamics of a target with free surface as well as of the resulting shock wave propagation that might be generated during the intense energy deposition. The results from the computer simulation will show whether a pressure wave is generated inside the liquid jet and in addition study the consequences of such shock wave on jet behavior. The magnitude of the pressure wave will determine the severity of jet breakup and distortion. In the case that a strong pressure wave is generated inside the jet and, as a result, the jet is broken into energetic droplets flying inside the magnet, the SPLASH code can then be used to study the droplet impacts on the chamber wall. 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