# Presentation: 501062

## Recent Progress to DesignHelical Cooling Channel

*MC Workshop @ BNL*
*K. Yonehara*

**Recent Progress to Design****Helical Cooling Channel**

*Katsuya Yonehara*
- Fermilab APC

- MCTF

## Targets in this talk

*Targets in this talk*

*The final HCC design is still on going. *
*But I will show some simulation results which may*
*indicate 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?*

## Simulation in ideal condition

*Simulation in ideal condition*

| parameters |  |  | Bz | bd | bq | bs | f | Inner d of coil | Expected
Maximum b | E | RF 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 coil

- RF cavity

- Window

**GH2**

- RF is completely
- inside the coil.

*v* ~ 0.97 c at 200 atm GH2

## Cooling simulation in ideal HCC

*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

## Conceptual picture of pre-cooler (design-1)based on MANX channel

*Conceptual picture of pre-cooler (design-1)**based on MANX channel*

- RF section

- HCC section

- RF section

- HCC section

- HCC section

- Magenta: RF coil
- Red: RF cavity
- Yellow: 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 mismatching
- in longitudinal phase space.

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

*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

## 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.

## Conceptual picture of pre-cooler (design-2)

*Conceptual picture of pre-cooler (design-2)*

- HCC

- Downstream
- Matching

- Upstream
- Matching

-  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...

## Using LiH absorber in design-2 pre-cooler

*Using LiH absorber in design-2 pre-cooler*

- coil

- GH2 filled RF cell

- LiH

- GH2

- coil

- LiH

- GH2

- 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

## 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

## Apply MANX channel for pre-cooler

*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. *

## 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. *

## What is next?

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