Yu. Senichev, on behalf of the JEDI Collaboration*

Transcription

1 Mitglied der Helmholtz-emeinschaft STORA RIN DM SIMULATION: MTHODS AND RSULTS Yu. Senichev, on behalf of the JDI Collaboration* 3. August 0

2 lectric Diole Moment and Standard Model In frame of SM among the not yet understood henomena are the reasons for the violation of the CP symmetry. But CP violation is the only nown mechanism that could elain the matter-antimatter asymmetry found in Universe. The electric diole moments (DM) of fundamental articles are ecellent robes of hysics beyond the standard model (SM), e.g. SUSY, since they allow for values within eerimental reach whereas the SM redictions are several orders below them. 3. August 0 Folie

3 Tomas-Bargmann, Michel,Telegdi equation with DM term The sin is a quantum value, but in the classical hysics reresentation the sin means an eectation value of a quantum mechanical sin oerator: d S dt S e B m g, d e e / 4 mc B e m MeV MeV sec.9979 m/sec 4d mc 5 ec e DM 0 3. August 0 Folie 3

4 Main roblems of DM simulation -the arithmetic corocessor has a mantissa length of 5 bits (minimum recorded figure~*0-6 ) and can mae a mistae in calculating sin rojections after i- th element if S i+ -S i <0-6. y S z S y -the required revolution time simulation is ~0 9 - high accuracy of simulation -8 ~ 0 rad er element Therefore we tae an aroach, where the DM signal is not imlemented, and only the induced error signal is studied. 3. August 0 Folie 4

5 Methods of sin-orbital motion investigation -COSY Infinity rogram; -Symlectic Runge-Kutta integrating; -Direct numerical integration of T-BMT differential equations; -Analytical aroach. 3. August 0 Folie 5

6 COSY Infinity rogram (M. Berz) COSY Infinity is a rogram for the simulation, analysis and design of article otical systems, based on differential algebraic methods. In the DM search, it is the only rogram which allows the sin-orbit motion of millions of articles to be simulated over a real time scale eeriment during n 000 seconds. At resent, we use the MPI (Message Passing Interface) version of the COSY Infinity rogram installed on a suercomuter with rocessors. At the initial stage of DM research, we use COSY Infinity to study the behaviour of the sin aberrations for a large number of articles and a long-time calculation. 3. August 0 Folie 6

7 Symlectic Runge-Kutta integrating (A. Ivanov) The integrating Runge-Kutta rogram is intended to model the sinorbital motion with fringe fields in elements and including the DM signal directly in the simulation. The algorithm used in the rogram is not as fast as COSY Infinity by several orders of magnitude. Therefore, we use it mostly to investigate a short-time henomenon for single article that does not require long calculation eriods. As a basic method for the tracing rogram, a symlectic Runge- Kutta scheme was imlemented from W. Oevel, M. Sofroniou, ( Symlectic Runge- Kutta Schemes II: Classification of Symmetric Methods, rerint, University of Paderborn, ermany, 996.) 3. August 0 Folie 7

8 S The DM search methods in Storage Ring:. Resonant method with initial sin orientation in ring S B; S={0,S y,0} and B={0,B y,0}. Magic method with initial sin orientation in ring S ; S ; S={0,0,S z} and ={,0,0} 3. August 0 Folie 8

9 In resonant method* the sin frequency is arameterized : e B m B using RF flier ~ e. In case of arametric resonance when observe the resonant build u: S z ( n) h ( e s h s) sin sn hn cos sn l rf rf B y L cir s ~ DM signal f rev ) t Advantage: the method can be realized in COSY ring Disadvantage: the high requirement to stability of f rf i( f rf s f f rf rev B y S y z ; 0,,,... T e- eriod of enveloe B y RF field we shall T f -eiod of fundamental oscillation Sz ma * A.Lehrach, B.Lorentz, W.Morse, N.Niolaev and F.Rathmann 3. August 0 Folie 9

10 3. August 0 Folie 0 Magic method for urely electrostatic ring In the magic method the beam is injected in the electrostatic ring with the sin directed along momentum S and S ; S={0,0,S z} and ={,0,0} at magic energy :, g B B m e S dt d S B B ternal fields DM 0 mag

11 3. August 0 Folie Magic method for urely electrostatic ring In the magic method the beam is injected in the electrostatic ring with the sin directed along momentum S and S ; S={0,0,S z} and ={,0,0} at magic energy :, g B B m e S dt d S B B ternal fields DM 0 mag

12 Magic method in urely electrostatic ring In urely electrostatic ring the sin of article with magic energy rotates with the same angular frequency as the momentum and it tilts u in the YZ lane due to the DM with angular rate d S e m Sdt y S z ARC y B =0 y electrostatic field S DM ARC 3. August 0 Folie

13 Sin tune aberration in urely electrostatic ring In reality the beam has energy sread γ mag Δγ and all articles move in different eternal field. Therefore the sin tune has the aberrations deendent on energy γ and trajectory r(t) of articles. d S dt e m c n 0 S vs energy vs field distribution At magic energy it is no recession of sin. For no magic energy γ mag Δγ 0 (, r) Sin tune aberration 3. August 0 Folie 3

14 Sin Coherence Time is time when RMS sin orientation of the bunch articles reaches one radian (YS,BNL), and it has to be > 000sec. During SCT each article erforms ~0 9 turns in the storage ring moving with different trajectories through the otics elements. y S z y At such conditions the sin-rotation aberrations associated with various tyes of sace and the time deendent nonlinearities start to lay a crucial role. S t 3. August 0 Folie 4

15 3. August 0 Folie 5 Sin tune aberration due to energy sread Longitudinal comonent rev orb z z orb T dt d S mc el d ds S mc el d ds / c m el orb s

16 RF cavity as first ste to increase SCT RF off: d S z e L cir S 0 z d m0c for Δ/=0-4 SCT=6300 turns, which is ~ msec. RF on: / / ma cos z Idea of using the RF cavity was eressed long time ago by many authors, for instance [ A.P. Lyseno et al., Part.Accel. 8, 5 (986) ]. d S d z e L m0c cir ma cos z Sz 0 The sin swing in a raidly oscillating field with RF frequency and it is bounded within a very narrow angle ~0-6 deendent on ma ~ / z s 3. August 0 Folie 6

17 RF on: Second order aroach of sin tune versus Δ/ However, in the second aroach versus momentum the average tune sin is not zero sz e m L cir 0c cos 3 cos z ma z e m L cir 0c 3 ma At (Δ/)ma=0-4 and an aial article the number of turns for SCT is ~6 0 7 turns, that is ~80 sec. sin drift term The code COSY infinity simulation sin oscillation ma 3. August 0 Folie 7

18 Off-aial article: Longitudinal-transverse couling in electrostatic storage ring The electrical deflector has the central field symmetry: n r M mv where angular momentum. Due to this fact the total energy can be reresented as the function of the coordinates : m W( r, r ) r M mr The radial motion is one dimensional motion in the field with the n effective otential, and the equilibrium radius: R M r const r eq 3. August 0 Folie 8

19 Off-aial article: influence on sin motion The article with different momentum oscillates with resect to different energy levels: COSY infinity tracing results for initial coordinates =0, y=0 and =3mm, y=0. Thus, RF cavity will not be able to reduce the oscillation of the sin for off-aial articles, since: e Lcir sz m c 0 3. August 0 Folie 9

20 quilibrium energy level modulation as method to increase SCT Following hysical logic the only solution to increase SCT is the modulation of the energy level itself relative of the magic level. For this urose, we have increase couling between longitudinal and transverse motion that is, aroach frequencies as close as ossible to each other. In result we have got SCT=400 sec COSY infinity tracing results for initial coordinates =0, y=0 and =3mm, y=0. 3. August 0 Folie 0

21 3. August 0 Folie Sin tune aberration vs momentum and aial deviation Assuming violation magic condition for non-reference article the sin tune aberration is defined: with orb orb orb s L L L mc e L L orb orb... R R

22 3. August 0 Folie Sin tune aberration vs momentum and aial deviation rouing the coefficients of owers u to second order, we obtain an equation having a arabolic form : with coefficients having a arabolic deendence on aial deviation R F R F c m el orb s,,,,, 0,, 5 3 3,,, R R R F R R R F

23 3. August 0 Folie 3 Sin tune aberration vs and Conve surface, or concave surface deends on the sign of s F, R F R F,,,,, +

24 Two stes to minimize the sin aberrations - The lattice with a comensation of the mutual influence of deflector arameters, and lattice arameters - The lattice must rovide the alternate change of the sin aberration surface from concave to conve and vice versa 3. August 0 Folie 4

25 First ste The maimum flatness of sin aberration surface is reached by choice of arameters of deflector, and α momentum comaction factor. After otimization: 0.94, 0.96 α= August 0 Folie 5

26 lectrostatic lattice consisting of electrostatic deflectors and electrostatic quadruoles Figure: Twiss functions of electrostatic ring for ring and one cell 3. August 0 Folie 6

27 Method realization Question is how to customize the required,? 3. August 0 Folie 7

28 Second ste: alternating sin aberration method The ring is equied with two tyes of deflector with ; and av ; av changing from one deflector to another. - In such otics is easier to achieve minimum sin aberration - Raising the field strength between the lates in even deflectors and reducing in the odd deflectors it effectively adjusts the required coefficients and. It allows to adjust the sin of aberration to minimum. 3. August 0 Folie 8

29 Alternating sin aberration method Another ossibility is the creation of the required otential distribution due to otential changes in striline deosited on the surface of the ceramic lates. n or n Such lates may be the additional corrective elements laced on the sides of the main deflector 3. August 0 Folie 9

30 The limit caabilities of alternating sin aberration method The sread due to final Δ/ it is imossible to remove comletely using the correct and only. Nevertheless the total sread of sin deflection angle does not eceed ±0.5 rad after billion turns, which one corresonds to a SCT about 5000 seconds. 3. August 0 Folie 30

31 Tracing results: We used differential algebra methods realized in COSY Infinity and integrating rogram with symlectic Runge-Kutta methods.. Cylindrical deflector: after 0 6 turns S rms 0.00 that is SCT~500 sec. Alternating deflector: after 0 6 turns S rms that is SCT~5000 sec 3. August 0 Folie 3

32 Conclusion: -we have studied the behavior of sin aberration in the structure and develoed techniques to minimize it; -one of the most effective methods is the alternating sin aberration; -the analytical model allows finding the general solution of the retention of aberrations within the values allowed SCT to have about 5000 seconds confirmed by COSY-Infinity. Nearest future lan: -3D shae deflector -sin-orbital tracing in 3 D deflector -including B field 3. August 0 Folie 3