# Presentation: 795725

## Beam Interaction with gas filled RF Cavities

- Alvin Tollestrup
- 11-30-2007
- BNL Workshop

## The black line is at E/P = 13.2 for breakdown in hydrogen.  This comes from Ue = eE λ and λ= 1/Nσ and the postulate that the physics depends only on the energy of the electrons at the point of collision.  A more useful variable is E/N where N is the # molecules.cm3.  E/N for breakdown = 4 10-16.

- The black line is at E/P = 13.2 for breakdown in hydrogen.  This comes from Ue = eE λ and λ= 1/Nσ and the postulate that the physics depends only on the energy of the electrons at the point of collision.  A more useful variable is E/N where N is the # molecules.cm3.  E/N for breakdown = 4 10-16.

## E/P is a measure of 

- E/P is a measure of
- E x distance between electron collisions with the atoms.  Doubling E and doubling the pressure should leave the physics the same.  This is generally measured in Volts/cm/mmHg

## Slide 4

## Some Cross sections for electrons on hydrogen

- Pi ro2   0.88 E-16

## Fractional energy loss / collision for electrons in Hydrogen

**Fractional energy loss / collision for electrons in Hydrogen**
- Bekefi & Brown.  PR112,159,1958.

- 0.5 E-3

## Inelastic cross sections

## Slide 8

## IONIZATION CROSS SECTION FOR e + H2

**IONIZATION CROSS SECTION FOR e + H****2**

## Example

**Example**

## Beam passes thru cavity at max Vrf as a delta function

- After a 1⁄4 cycle the electrons have all drifted upwart by a distance deltaZ.  This discharges the top plate and leaves a layer of positive charge against the bottom.  The field in this region remains the same and the field outside decreases.  A 1⁄4 cycle later the image is reversed.

## Slide 12

## Slide 13

## 967 psia

- Does the calculation of mobility work at high density?  E/P being considered for muons is of order 10.

## Mobility correct?

- Fig. 5 shows the charge collected for alpha particles for various gas pressures and drift fields.  The peak point in MuonsInc plot is at 600 KV / cm  and 54 atm and is far off scale to the right indicating almost complete charge collection.
- Fig.6  shows data on the mobility of electrons in high pressure hydrogen.  The red point is calculated from the theory of  Crompton and Sutton.

- Data from Kammel at PSI

**IS RECOMBINATION TAKING PLACE**?

**Mobility correct?**

## EXAMPLE FOR HCC

- The next slide gives the input data for the three cases.

**EXAMPLE FOR HCC**

## 3 Examples from HCC:

| Emittance | 4.3 mm rad | 1.5  mm rad | .91  mm rad |
| --- | --- | --- | --- |
| Freq | 400 Mhz | 800 Mhz | 1600 Mhz |
| Beta function | .42 m | .26 m  | .15 m |
| Gradient | 16 MV/m | 16 MV/m | 16 MV/m |

| Beam rms r | 27.6 mm | 12.8 mm | 7.6 mm |
| --- | --- | --- | --- |
| Cavity length | 5.0 cm | 2.5 cm | 1.25 cm |
| Q from plasma | 483 | 553 | 392 |
| Joules Cav | 5.7 | .72 | .09 |

- H gas density = .017 rgm/cm^3 = 200 atm at 270 deg C.
- Beam pulse 10 e10 per bunch 10 bunches = 10 e11 total
- 800 Mhz cavity radius 15.6 cm.  Scaled with Freq.

| Joules gas/cycle | .075 | .0082 | .0014 |
| --- | --- | --- | --- |
|  |  |  |  |
|  |  |  |  |

## 400 Mhz

**400 Mhz**

## 800 Mhz

**800 Mhz**

## 1600  Mhz

**1600  Mhz**

## Slide 21

##  s = E  eo  ;  For instance 100 KV/meter requires a surface charge of 88 pC 

-  **s = E  eo  ;  For instance 100 KV/meter requires a surface charge of ****88 pC **
**A factor of 10****6 **** less****  ****than the total charge in the ions.**

## MTA Test

- Consider 800 Mhz cavity in linac beam:
- 1.  Bunch spacing 5 ns and 0.13 ns wide with about 10 e9/ bunch or less.  So the bunches are delta functions crossing every 4th cycle.  We assume that the cavity is synched to the linac.  The first couple of bunches may be smaller as the batch gets gated on.  There can be up to 1000 bunches for a total to 1.7 10e12 protons with βγ=1 for a dE/dx= 6 MeV/gm/cm2 or 1.5 times min.  So each bunch is equivalent to
- 2.5  10e9 mip.  Using the numbers from slide 2 of 8.2 10e-3 joules loss/cycle for 10e11 mip we get for 4 cycles and 1 bunch:
- 		4  2.5 109   8.2  10-3 / 1011 = 8.2 10-4 joules/4 cycles (or bunch)
- 		Energy stoired in cavity = .72 joules
- So the energy loss/bunch is like the single bunches of 1010 particles but spread over 4 cycles.  So one will be able to measure the loading of the cavity by the beam by measuring the loading of the cavity which increases linearly thru the linac pulse.
- Maybe one wants to turn off power to cavity before beam hits and watch it decay in order to measure loading.

## Slide 24

## Slide 25

## Questions and things to measure

- What is the mobility at high pressures?
- Can we get an estimate of the recombination rate?  How long do the ions hang around?  Does it matter?
- What is the recombination time with a little SF6 added?                               	   1/n1 dn1/dt = R  n2   If the right side is 109  and n2 is 1% of the hydrogen (X0 SF6 is 1/150 XH)  n2 = 1022  /100  Then R = 10-11  This R seems to be in range I can find for various processes.
- Need measurements for narrow beam and high intensity as exist at end of cooling change.
- Open cell cavities are different.  There is a column of plasma and no end electrodes.  B keeps the plasma from diffusing  in radial direction very fast so at peak of cycle there are blobs of positive charge between cells.

## The linac has 10 μSec pulse.  Is there any way to get single bunches?

- A small light pipe leading out of the cavity to observe light could be useful.

## See “Example” for conditions other than density.

## Slide 29