1December 6, 2007 MC Workshop @ BNLK. Yonehara

1

Recent Progress to DesignHelical Cooling Channel

Katsuya YoneharaFermilab APC

MCTF

22

Targets in this talk

The final HCC design is still on going. But I will show some simulation results which mayindicate some clues to breakthrough some crucial issues:

• End-to-end HCC design

– Combining RF section in HCC will be discussed. – It strongly relate with pre-cooler design.

• What’s next?

33

Simulation in ideal condition

parameters Bz bd bq bs fInner d of

coilExpected

Maximum b ERF

phase

unit m   T T T/m T/m2 GHz cm T MV/m degree

1st HCC 1.6 1.0 -4.3 1.0 -0.2 0.5 0.4 50.0 6.0 16.4 140.0

2nd HCC 1.0 1.0 -6.8 1.5 -0.3 1.4 0.8 30.0 8.0 16.4 140.0

3rd HCC 0.5 1.0 -13.6 3.1 -0.6 3.8 1.6 15.0 17.0 16.4 140.0

•Use a pillbox cavity (zero-thickness window this time). •RF frequency is determined by the size of helical solenoid coil.

To realize practical condition: •The pressure of gaseous hydrogen is 200 atm at room temp to realize the practical RF field gradient.•The operation temperature in an absorber container can be low, i.e. LN2 temp. •Required gap between a coil and a RF cell is 20~30 mm which includes supports, a cell wall, and a thermal isolation shield. •Additional space is needed for a RF feed line (20~25 mm).•Pressurized wall is needed (it may be an outer shell of channel).

Helical solenoid coilRF cavity

Window

GH2

RF is completely inside the coil.

2.405

2

vR

f v ~ 0.97 c at 200 atm GH2

44

Cooling simulation in ideal HCC

•The transmission efficiency is 50 %. Caused by a transverse mismatching in between HCCs. •This can be improved by using a smaller frequency step.

Start point

•There is a missing link between a start point and an acceptance of 1st HCC. A pre-cooler is needed (following section). •We need to occupy another missing link at lower emittance.

HCC goal

5

Conceptual picture of pre-cooler (design-1)

based on MANX channel

5

RF section

HCC section

RF section

HCC section

HCC section

Magenta: RF coilRed: RF cavityYellow: HCC coil

HCC section: • kappa = 1.0• lambda (m) = 1.6,1.2,1.0,0.8…• No RF• Small coil gap to make an ideal field• Filled with LH2

RF section: • kappa = 1.0• lambda (m) = 1.6 • Large coil gap to put the RF cavity• Filled with GH2• Gas pressure = 100 atm @ 300 K, This scheme can relax some problems caused by a pressurized gas.

I stacked this design. Problem is caused by the mismatchingin longitudinal phase space.

6

Momentum-time phase space advance in design-1 cooling section with three different

field configurations

Two clear indications• HCC can be more isochronous by tuning the dispersion. • However, it makes less longitudinal phase space cooling. dp slope gets smaller at stronger isochronous condition.

Geometric parameters: =1.6 m, =1.0, LH2 absorber

7

Problem in RF section

• (top layer) dp-dt in 0-crossing RF• (bottom layer) dp-dt in 100 atm GH2 RF =1.6 m, =1.0, Erf = 20 MV/m, rf = 150 degree

The phase advance in HP GH2 RF is asymmetric. This causes mismatching. We need further studies or it may not be the best choice for pre-cooler.

8

Conceptual picture of pre-cooler (design-2)

8

HCCDownstreamMatching

UpstreamMatching

• Gap between coils = 0.04 m• Current = 1075.0 A/mm2

Track of reference particle

GH2

LHe

beam

RF cavity

Window (Be)

Helical solenoid coil(SC or HTSC)

Pressurized wall

•Put RF cavity in between coils.•Required gap can be 100 mm.Thermal isolation+supports+cell wall…

9

Using LiH absorber in design-2 pre-cooler

coil

GH2 filled RF cell

LiH

GH2

coil

LiHGH2

RF cell is invisible in those pictures.

•kappa = 1.0• lambda (m) = 2.0 m• helical radius = 0.32 m• inner coil radius = 0.33 m• coil thickness = 50 mm

•GH2 pressure = 100 atm•LiH thickness = 2.0 mm•Erf = 40 MV/m,rf= 153 degree•frf = 325 MHz•RF length = 100 mm

10

Simulation result in design-2 pre-cooler

•Wiggler at beginning is happened by mismatching and statistic error. •Reaches the equilibrium at z=30 m.•6D cooling factor is 8 which is slightly smaller than the previous simulation result. This may be caused by LiH.

•Design-2 pre-cooler completely satisfies the initial gap.

HCC goal

1111

Apply MANX channel for pre-cooler

• Do MANX experiment to test 6D theory and validity of simulation.

• Helical solenoid coil is designed a segment structure to generate tapered field.

• Probably we can replace some segments to a RF cell.

12

Conclusions

• A pre-cooler design has been investigated.

• Design-2 seems to be better than design-1.

• 6D cooling is demonstrated in LiH channel.

• MANX can be used as a pre-cooler by re-forming helical coils and put RF cells in between coils.

12

13

What is next?

• Test LiH in normal HCC. • Study low emittance HCC. • Reform MANX to put the RF cell

in the magnet.