# Presentation: 036345

## INJECTION PAINTING, FOIL& TARGET DISTRIBUTION

**Joanne Beebe-Wang**
***BNL, Upton, NY 11973, USA***

**September 13, 2000**

**SNS ASAC Review**

## Introduction

- What is injection painting:
- 	It is an injection with a controlled phase space offset between the centroid of injected beam and the closed orbit in the ring to achieve a different particle distribution from the injected beam.
- Why injection painting for SNS:
-     to satisfy target requirements
-     to reduce beam losses due to space charge
-     to reduce foil hits (foil life-time, beam loss at foil)** **

- Joanne Beebe-Wang

## Basic Painting Schemes

- Correlated painting	Anti-correlated painting

- Joanne Beebe-Wang

## Analytical Expression

- It is a 4-D problem (*x, x’, y, y’*).  But, if
- 1) distribution of injected beam can be expressed as
*     **n(x,x’,y,y’)=n**x**(x,x’) n**y**(y,y’)*
- 2)  the bump in (*x, x’*) phase space moves independently from (*y, y’*),
- it becomes a 2-D by 2-D problem.
-     In normalized *x, p**x* phase space, if
-         -           changes slow compare to betatron oscillation, particles injected at *P* paint the same phase space as particles injected at *P**1* .
-     Maximum x is determined by the particles injected at *Q*.

- Joanne Beebe-Wang

## Analytical Expression (continued)

- Particle distribution due to transverse phase space painting:
- for a single particle:
- If the distribution of injected beam is Gaussian with 0x and 0y
- where
- where *I**0**(z)* is the modified Bessel function of order zero, and
- 				             center offset ( x0(t), x’0(t))

- Joanne Beebe-Wang

## Analytical Expression (continued)

-      Very high local density at the center of the beam if        x(t)=y(t)=0.  So, one should not have zero offset in 4-D phase space any time.
-      Correlated painting will give a rectangular shaped beam distribution with high density along the diagonal line, and low density on the x- and y-axis.
-      If ***0x** << **** x(t)* and ***0y** << **** y(t),* anti-correlated painting with offsets *** x(t) = A t**1/2 **, **** y(t) = B (t**inj **-t)**1/2* will give a KV-like particle distribution at time *t**inj* .

**Analytical Expression (continued)**

- Joanne Beebe-Wang

## Basic Painting Schemes

- Correlated painting with/without space charge
- x=5.82              y=4.80
- inj,x=4.93m  inj,y=7.24m
-  inj,x=0.11       inj,y=0.07
- inj. RMS,Nor=0.5mm-mr Final =120 mm-mr

- Joanne Beebe-Wang

##  Basic Painting Schemes

- Anti-correlated painting with/without space charge
- x=5.82              y=4.80
- inj,x=4.93m  inj,y=7.24m
-  inj,x=0.11       inj,y=0.07
- inj. RMS,Nor=0.5mm-mr Final =120 mm-mr

- Joanne Beebe-Wang

## Basic Painting Schemes

- _painting scenarios__	__	__correlated__	__anti-correlated_
- Beam shape without SC		Rectangular	Oval
- Beam emittance evolution		Small to large	~ constant
- Final emit. x+y(mm-mr)		120+120		160
- Foil-hit rate (11 linac dist.) 	 	6.1  8.3		8.0  10.5
- Max foil temp. (K) (11 linac dist.) 	2113  2273	2248  2376
- Horizontal aperture (H )		1:1		1:1
- Vertical aperture (V )		1:1		1:1.5
- Susceptible to coupling 		Yes		No
- Capable for KV painting		No		Yes
- Paint over halo 			Yes		No
- Horizontal halo/tail		Normal		Normal
- Vertical halo/tail			Normal		Large
- Satisfy target requirements		Likely		Not likely
- Bump function 			Square root;	Square root;
-     candidates 			exp(-t/0.3ms);	exp(±t/0.6ms);
-     for optimization			Combination	Sinusoidal

- Joanne Beebe-Wang

## Injection Bump Optimization 

- Joanne Beebe-Wang

## Foil Heating & Foil Miss

- Injected Beam Distribution       Foil Temperature [K]

- Joanne Beebe-Wang

## Foil Heating & Foil Miss (continue)

- Injected Beam Distribution      Foil Temperature [K]

- Joanne Beebe-Wang

## End to End Simulation

- Foil Miss, Foil Hit & Foil Temperature

- Joanne Beebe-Wang

## Foil Lifetime Tests on BNL linac

-   Lifetime = 5-80hrs on BNL linac depending on foil thickness, fabrication and mounting methods
-   SNS repetition rate = 9 BNL linac repetition rate
-   Maximum 24 foils on the foil changing chain

**Foil Lifetime Tests on BNL linac**

## Foil Heating & Scattering

- Joanne Beebe-Wang

## Foil Hits & Beam Loss

- 	Beam loss as a consequence of foil traversal through the following mechanism:
-    (1GeV proton, foil=300g/cm2, foil traversal rate=7hits/particle)
- Nuclear Scattering
- 	estimated fractional loss=3x10-5
- Particle loss in gap due to energy straggling
- 	estimated fractional loss=3x10-6
- Transverse emittance growth due to multiple Scattering
- 	estimated =4x10-2 mm-mr

- Joanne Beebe-Wang

## Radiation due to Nuclear Scattering

- Particle Loss (Fraction)        Radiation at Injection Area

## Injection Beam Loss 

-       Major sources of beam loss that go to the injection dump:
-   Foil Inefficiency (FI)
-    Foil 400200g/cm2
-          FI = 210%
-   Foil miss (FM)
-    (see figures)
-    Injection dump limit:
-        FM + FI  10%

**Beam loss caused by injection errors:**

- Transverse position                     Linac emittance error
- error c at injection                      =inj-0.5 mm-mr

- Joanne Beebe-Wang

## 
	There could be three kinds injection errors caused by injection mismatch. They cause emittance growth in the circulating beam.
	Current design: UN=120mm-mr, inj,y=7.24m, inj,y=0.042, p/p=0.25%
Steering Mismatch										Expected x = 0.2 mm, x’ = 0.2 mrad					RMS,UN =0.9 mm-mr
Dispersion Mismatch
					Designed D = 7 cm, expected D’= 0.02
						RMS,UN =0.004 mm-mr
 -function Mismatch
					Expected /M =  /M = 0.025
      					RMS,UN =0.02 mm-mr
	The impact on circulating beam emittance growth is negligible. 

- 	There could be three kinds injection errors caused by injection mismatch. They cause emittance growth in the circulating beam.
- 	Current design: UN=120mm-mr, inj,y=7.24m, inj,y=0.042, p/p=0.25%
- Steering Mismatch										Expected x = 0.2 mm, x’ = 0.2 mrad					RMS,UN =0.9 mm-mr
- Dispersion Mismatch
- 					Designed D = 7 cm, expected D’= 0.02
- 						RMS,UN =0.004 mm-mr
-  -function Mismatch
- 					Expected /M =  /M = 0.025
-       					RMS,UN =0.02 mm-mr
- 	The impact on circulating beam emittance growth is negligible.

- Joanne Beebe-Wang

## Target Distribution

- Beam requirements at the target

- Joanne Beebe-Wang

## Conclusions

- Simulation shows that correlated painting has better chance to meet the target requirement and may minimize halo.  Anti-correlated painting causes excessive halo at full intensity.
- Halo/tail driven by space charge and magnet errors can be reduced by splitting tunes.
- Injection error increases foil-miss rate which causes increased dump load and decreased beam power.  Its impact on beam emittance growth is negligible.
- Injection , -function mismatch can reduce foil heating.  It can also be used to reduce the foil traversal rate for increased linac emittance.

- Joanne Beebe-Wang