# Presentation: 760977

## Carbon Wire Heating due to Scattering in the SNS 

**By**

**C. J. Liaw, BNL**

**July 17, 2001**

**SNS Wire Scanner Preliminary Design Review**

## Assumptions

**Assumptions**

** ****Beam Energy:**
-     ***Injection Line***: H- beam, From 2.5 MeV (MEBT)  to 		    1.0 GeV (HEBT)
-     ***Accumulator ring & RTBT***: 1.0 GeV  Proton beam
** ****Beam profile:**
- 	2-D Gaussian distributed in the injection line
- 	Quasi-uniform in the ring & RTBT

## Assumptions

**Assumptions**

_**Carbon wire**_
***Size***: 32 m dia.
**Stationary at the center of the beam***** ***

## Assumptions

**Assumptions**

_**Possible wire heating scenarios in the injection line**_
***Beam currents over a pulse****:*
- 16 mA (1 MW case) and 36 mA (2 MW case)
***Repetition rate and pulse length****:*
- 60 Hz,1 ms long
- 6 Hz, 1 ms long
- 6 Hz, 50 s long

## Slide 5

## Slide 6

## 	Increase from  3.1 mm x 3.8 mm to 56 mm x 68 mm in 1 ms or	Cross section area A = 6.45 x 10-6+3.09*t  [m2], where t = time [sec]

-  ***Beam current over a pulse:***
- 	16 mA (1 MW case) and 32 mA (2 MW case)
-  ***Repetition rate and pulse length: 60 Hz and 1ms long***
** *****Beam size (H x V):***
- 	Increase from  3.1 mm x 3.8 mm to 56 mm x 68 mm in 1 ms or	Cross section area A = 6.45 x 10-6+3.09*t  [m2], where t = time [sec]

**Assumptions**

_**Wire heating in the ring**_

## Assumptions

**Assumptions**

-  ***Beam current over a pulse****:*
- 	16 mA (1 MW case) and 32 mA (2 MW case)
-  ***Repetition rate and pulse length: 60 Hz and 695 ns long***
-  ***Minimum beam size (H x V): 56 mm x 68 mm***

_**Wire heating in RTBT**_

## Assumptions

**Assumptions**

_***Radiative cooling is the only cooling mechanism***_***.***** **
_***Thermal properties of carbon***_***:***** **
- Density = 2000 kg/m3
- Radiant emissivity = 0.8
- Heat capacity (temperature dependent)

## Carbon Heat Capacity

**Carbon Heat Capacity**

## POWER DEPOSITION ON THE CARBON WIRE

-  ***For 2.5 MeV  ~ 1 GeV H******-****** beam:***
- 	P = 1/(dE/dx)p I x + 2 Pe		 [watts/m2]
-  ***For 1 GeV proton beam:***
-        P = 1/(dE/dx)p Ix			[watts/m2]
- where  Pe = 1/(dE/dx)e Ix	(1/(dE/dx)ex < Ps)
-                 = Ps  		(1/(dE/dx)ex >= Ps)
-             Ps = power to stop an electron beam [eV],
-             I  = beam current density [A/m2]
- 1/dE/dx)p  and 1/dE/dx)e  =   Collision energy loss of the proton and the electron beam through the carbon wire [MeV/g/cm2].

**Beam Energy Loss Due To Scattering**

## dE/dx of H- beam through carbon wire

**dE/dx of H****-**** beam through carbon wire**

## Heating Efficiency of Carbon Wire, 

**Heating Efficiency of Carbon Wire, ******

## Power Deposition On The Carbon Wire

- Pd         =          P          x         

- Deposition power density

- Beam energy loss density

- Heating efficiency

## Governing Equation

**Governing Equation**

**dT/dt = 4/(********dc)*(P********-********(T****4****-T****0****4****)) **
- where ** ** T = wire temperature  [K]
-              To = beam pipe temperature = 297 [K]
-              d = diameter of the wire  [m]
-               t = time  [sec]
-               = heating efficiency
-               Stefan Boltzmann constant5.67 x 10-8 [W/m2K4]
-               , , c, and P are defined above.

## Max. Wire Temperature In The Injection Line (1 MW case)

**Max. Wire Temperature In The Injection Line (1 MW case)**

## Max. Wire Temperature In The Injection Line (2 MW case)

**Max. Wire Temperature In The Injection Line (2 MW case)**

## Maximum Wire Temperature In The Ring

**Maximum Wire Temperature In The Ring**

***Stationary or crawling wire****:*
- 1 MW case:  398 K
- 2 MW case:  450 K

## Maximum Wire Temperature In RTBT

**Maximum Wire Temperature In RTBT**

***Stationary or crawling wire:***
- 1 MW case: 396 K
- 2 MW case: 460 K

##  Carbon wires will survive (i.e.: wire temperature < 2000 K) in the entire injection line with a 6 Hz/50 s H- beam and can only be used in the higher energy region with the 6 Hz/ 1 ms and 60 Hz/1 ms H- beam.

-  Carbon wires will survive (i.e.: wire temperature < 2000 K) in the entire injection line with a 6 Hz/50 s H- beam and can only be used in the higher energy region with the 6 Hz/ 1 ms and 60 Hz/1 ms H- beam.
-  The wire temperatures in the ring and RTBT are low.   Lifetime of the carbon wire is not an issue in these regions.

**CONCLUSIONS**