1. Chopper Beam Dump Thermal Problem 10/27/20101PX Linac FE Technical Discussions

2. 10/27/2010PX Linac FE Technical Discussions2 Beam deflection is only in one plane. With full power of the beam 25 kW, the first dump loss is ~2.5 kW, The second dump loss is ~16 kW, the third dump loss is ~6 kW, and the fourth dump is ~0.5 kW. Low loss in the two last dumps is to solve extinction problem. The first dump loss is two low – can be avoided. More dumps can be inserted if needed to reduce power Longitudinal space available for one dump is ~200 mm. Distance from the axis to the dump is ~6 mm. From the First Presentation on the Issue: (June 30, 2010)

3. 10/27/2010PX Linac FE Technical Discussions3 Current Density in the Beam Relative current density distribution in the beam before the first chopper { [mA/mm 2 ] and [mm]} J[mA/mm 2 ] = 0.1/(1+e (r-5.3) /0.8) Having analytical expression allows calculation of heat deposition in the targets: 1-st BD – 10% loss 2-nd BD – 50% loss This is in agreement with the data from N.S. Maximum power density in the beam is 250 W/mm 2

4. 10/27/2010PX Linac FE Technical Discussions4 Initial Understanding of the Problem Copper: Tmin = 273 K, Tmax = 353 K Water: Tmin = 273 K, Tmax = 275 K Laminar flow in a thin slot P = 0.25 W/mm^2 -- Compare with the required ~10 W/mm^2 Using turbulent regime improves the situation but not to the required extent. It allows incident power densities up to ~0.6 W/mm^2

5. Proposed way to solve the cooling problem 1. The reason of poor cooling capacity is poor thermal conductance of water 2. Turbulence helps to make the transition layer thinner, thus improving the situation 3. Using good thermal conductance of metal body of the heat exchanger helps to deliver heat to many channels 4. Using many thin wall channels helps to increase the surface area 10/27/2010PX Linac FE Technical Discussions5 For a fixed hole distribution pattern, the number of holes per unit of area is in reversed proportion to the hole diameter (N1~1/d 2 ). Combined perimeter of the holes per unit of area is then P1 ~ 1/d So, the smaller hole can be made – the larger heat exchange surface area can be obtained.

6. Example 10/27/2010PX Linac FE Technical Discussions6 Slice of the cooling plate (perpendicular to the beam propagation direction) Power deposition though the bottom Temperature distribution across the slice (vertically) Power density is 6 W/mm 2 This corresponds to the required surface tangent of ~1:40

7. Optimal diameter of the holes For holes ~0.5 mm in diameter and water velocity in the channels of 2 m/s, water pressure is low (~8000 Pa), but the flow is quite high (~10 GPM for the 200-mm device). Smaller hole diameters will lead to higher pressure and lower flux. We can impose a limit to pressure of ~1 bar (or ~100,000 Pa). 10/27/2010PX Linac FE Technical Discussions7

8. Optimal diameter of the holes 10/27/2010PX Linac FE Technical Discussions8 Flux though the pipe in the laminar regime By reducing the radius by factor of 2,with the same pressure drop, we get 16 times lower flux though one hole, but the number of holes per unit are is higher by factor of 4. So we will have 4 times lower total water flux through the device. Total cross-section are of the holes in the device will be the same. Total heat exchange area will be 2 times larger.

9. Sample 2 10/27/2010PX Linac FE Technical Discussions9 Input Pressure – 100,000 Pa P1 = 10 W/mm 2 Total water flux -- 6.7 GPM Re = 1000

10. Verification Things look too good so far. Nevertheless additional cross-check is required. 10/27/2010PX Linac FE Technical Discussions10

11. Alternative Approaches. I 10/27/2010PX Linac FE Technical Discussions11 Length of the beam dump25 cm 5 holes in the copper matrix (series hydrauilc connection) Max. linear power density1 kW/cm Water pressure drop2 atm. Length of all (incl. connection) pipes2.5 m Water flow1.1 l /s (17.5 GPM) Average water velocity7.2 m/s Average water temperature rise5 K Required heat density influx into water channels 45 W/cm 2 Total area of the walls560 cm 2

12. Alternative Approaches. II To insure the needed heat influx, the temperature gradient in water near the walls must be ~10 K/cm. Geometrically, this value looks OK, but proper conditions must be created for the water flow so that the needed power can be transferred into the body of water, which has very low thermal conductance of just 0.6 W/m-K. The main problem can be that the wall temperature exceeds 100° C 10/27/2010PX Linac FE Technical Discussions12

13. Critical Heat Flux http://resources.metapress.com/pdf- preview.axd?code=r11nw30g75366n20& http://resources.metapress.com/pdf- preview.axd?code=r11nw30g75366n20& Critical heat density of the flux (transition from nucleate boiling to film boiling) is measured to be in the range from 0.7 W/mm 2 to 1.2 W/mm 2 From this point of view, the power density used by Valery is also OK. 10/27/2010PX Linac FE Technical Discussions13

14. Alternative Approaches. III Using thin channels can be somewhat advantageous because it can help to increase reduce the required water flux. Using thick-wall axially symmetrical dump structure suggests significant simplicity and some freedom of choosing the cooling scheme. All the scheme require honest analysis first. Making a prototype and testing it using e-beam must also be considered. 10/27/2010PX Linac FE Technical Discussions14