Status of Low- FOFO Snake for Final Stage of 6D Ionization Cooling - PowerPoint PPT Presentation

Status of Low-  FOFO Snake for Final Stage of 6D Ionization Cooling Y. Alexahin (FNAL APC)  This work is a continuation of effort reported at MCDW’09 (BNL) and NFMCC’10 (Miss. Univ.) and resumed now after a 3 year hiatus  Is it worthwhile? MAP vacuum RF cooling mini-workshop, FNAL, September 18-19 2013

2 Motivation + - + “cell” B [T] B z 10 FOFO snake with phase advance B y  10 >180  /cell has a number of attractive 5 features: z [cm] 10 20 30 40 50 60 70 5  Apparent technological simplicity (RF 10 between solenoids, not inside)  [cm]  Potentially higher compactness: phase 25 advance / absorber (  +) is somewhat  y  x 20 smaller than in RFOFO (3  /2-) 15 10 - However, phase advance / period (2  +) 5 is higher creating problems with beam z [cm] 10 20 30 40 50 60 70 dynamics. D [cm] D y 2 z [cm] 10 20 30 40 50 60 70 2 4 D x 6 Low-beta FOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

3 Problems with Low-Beta FOFO Snake  Dispersion = 0 at focal points  stronger transverse field is required  Large difference in cooling rates of the two transverse normal modes  Momentum acceptance limited from above by sign change in the slippage factor  Momentum acceptance limited from below by fast increase in the ionization loss rate   p        0 K ( ) [ 1 ( ) ] d   p ( ) The major mechanism of losses is diffusion over the maximum of long. “kinetic energy” – 0.0030 change of the slip factor sign at higher values 0.0025 of momentum. 0.0020  = L (  p )/ L (0) – relative length of the periodic p0 = 100 MeV/c 0.0015 orbit 0.0010 p0 = 120 MeV/c 0.0005 0.10 0.05 0.05 0.10 0.15  p  Maximum   is reached between solenoids where the field nonlinearity is also at maximum:   3 3 ~  B B  r z 3 3 r z This creates difficulties with the transverse acceptance as well Low-beta FOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

4 Geometry & Parameters - + 16cm 2  8cm open cell 600 MHz Rout= 38cm RF cavities, Emax=18MV/m 16cm Rin= 14.5cm 38cm 2cm LH2 absorber with 18  LiH wedges making use of large D y  Total length of 2-cell period 2  38cm = 76cm Bz_axis=11.5T (Bz_coil=17.3T, j < 200A/mm 2 ) for p 0 =100MeV/c, constant By=0.01T The transverse modes cooling rates can be equalized by 1-periodic quadrupole field with gradient 1.1T/m between the solenoids (proposed by R.Palmer difference in solenoids also works but makes transition worse). Normal mode tunes (including cooling rates) and normalized equilibrium emittances: tune* 1.229 + 0.00149 i 1.245 + 0.00144 i 0.109 +0.00042 i  N (mm) 0.183 0.201 1.03 *) Transverse phase advance / period is (almost) 2.5  Low-beta FOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

5 G4BL Tracking  p/p0 px/p0 py/p0 0.6 0.6 0.2 0.4 0.4 0.1 0.2 0.2 0.2 0.2 0.4 0.6 4 2 2 2 2 4 y (cm) t (ns) x (cm) 0.2 0.2 0.1  z  0.1ns*v  2cm 0.4 0.4 Evolution of the initial Gaussian distribution truncated at 3sigma (blue dots) over 100 periods (76m) - red dots N  z (cm) 0.08 10000 9500 decays 0.06 quadrupole not off  2 (cm) 9000 strong enough! 0.04 8500 8000 0.02  1 (cm) 7500 10 20 30 40 50 60 70 10 20 30 40 50 60 70 z (m) z (m) Normalized emittances (Gaussian fit) and intensity over 100 periods . Final   =0.21mm, total losses (with decay) = 40%. Low-beta FOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

6 Cooling Efficiency Q 6D R. Palmer’s 6D quality factor decays 10  included d log  6 D Q 6 D d log N 5 Average value Q 6D  3 10 20 30 40 50 60 70 z (m) I tried to improve transmission by:  Larger wedge angle (25  ) – opposite result (!?)  Changing tunes: ~ constant for 1.2<Q  <1.25, big drop for Q  <1.2 (Q  -2Q s SBR?) and Q   1.375  Rotation of LiH wedges to utilize both D y  and D x – no effect  Lower momentum (90MeV/c) – no effect (this is actually good!)  Deceleration from 100 to 90MeV/c over 50 periods – opposite result  Higher RF frequency (650MHz) and higher voltage (20MV/m) – opposite result (Q  -2Q s SBR?)  Lower RF frequency (325MHz) and triangular pulse equivalent to 150MHz (this should also reduce space-charge effects) Low-beta FOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

7 325 MHz RF N continuing “shaving” 10000 due to insufficient  z (cm) 9000 momentum acceptance decays off 0.10 8000 7000 0.08 6000 0.06 quadrupole  2 (cm) 20 40 60 80 100 Q 6D 50% stronger 0.04 10 decays on  1 (cm) 0.02 5 z (m) 20 40 60 80 100 20 40 60 80 100 Normalized emittances (Gaussian fit), intensity and 6D quality z (m) factor over 150 periods (114m). 5 Final   =0.17mm, total losses (with decay) = 60%. 10  p/p0 0.2 0.1 bunch length increase is smaller than expected 0.2 0.2 0.4 0.6 t (ns) 0.1 Low-beta FOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

8 Summary  Low-beta FOFO-snake with LiH wedges does work allowing for normalized transverse emittance < 0.2mm  Equalization of the transverse normal mode cooling rates can be achieved with either the solenoid current difference or a weak periodic quadrupole field (<2T/m)  The major performance limitation is imposed by insufficient momentum acceptance  There are still some possibilities to explore in order to improve transmission – may take a week more to exhaust them Low-beta FOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

325 MHz Helical FOFO Snake for Initial Stage of 6D Ionization Cooling Y. Alexahin (FNAL APC) MAP vacuum RF cooling mini-workshop, FNAL, September 18-19 2013

2 Basic Idea alternating solenoids absorbers RF cavities • The idea: create rotating B  field by periodically tilting solenoids, e.g. with 6- solenoid period. • Periodic orbits for μ + and μ - look exactly the same, just shifted by a half period (3 solenoids). B [T] • With tune Q  >1 (per period) r  D >0 B x  50 B y  50 B z  muons with higher momentum make a longer path  longitudinal cooling achieved even with planar absorbers z [cm] y x, y [cm] y x x z [cm] Periodic orbit for p=200MeV/c HFOFO Update - Y. Alexahin NUFACT09, IIT Chicago July 22, 2009

11 Optics Functions B [T] 4 B x  100 B y  100 B z 2 50 100 150 200 250 300 350 z [cm] Total length of 6-cell period = 372cm vs 612cm @200MHz 2 – I tried to reduce   as much as reasonably possible 4 Bz_axis=3.8T (j < 200A/mm 2 ) for p 0 =200MeV/c, solenoid  [cm] pitch angle 5mrad  y 55 The transverse modes cooling rates are equalized by 50 costant quadrupole field with gradient 0.12T/m 45 40 Normal mode tunes (including cooling rates) and 35 normalized equilibrium emittances:  x 30 tune 1.21 + 0.0069 i 1.24 + 0.0069 i 0.16 +0.0031 i 25  N (mm) 2.47 2.39 3.48 50 100 150 200 250 300 350 z [cm] D [cm] D y D x 40 20 50 100 150 200 250 300 350 z [cm] 20 40 325MHz HFOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

12 G4BL Tracking  p/p0 px/p0 py/p0 1.0 0.8 0.5 0.6 0.5 0.4 20 10 10 20 x (cm) 20 10 10 20 0.2 0.5 y (cm) 0.5 0.5 1.0 0.5 t (ns) 1.0 0.2 2.5 Initial Gaussian distribution includes all correlations up to 2 nd order (including energy-transverse 2.0  z (cm) amplitude^2) 1.5 Horizontally beam extends over 20cm, transverse  2 (cm) momentum exceeds p0=200MeV/c! - inevitably 1.0  1 (cm) high losses in the beginning (next slide) 0.5 20 40 60 80 z (m) Normalized emittances (Gaussian fit) over 25 periods (93m) . Final   =3.5mm,  || ~ twice larger 325MHz HFOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013

13 Cooling Efficiency Q 6D N 30 decays on 5000 25 20 4500 decays off 15 4000 10 5 3500 20 40 60 80 z (m) z (m) 20 40 60 80 Final value of Q6D exceeds 20 – cooling can be continued. Now I should try Dave’s rotator output. 325MHz HFOFO snake – Y.Alexahin, MAP mini-workshop, Fermilab, 09/18/2013