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Black Body Radiation Shields

Jan 15, 20255 min read

Goal:

To cooldown to lower temperatures we must reduce heat load sources on our 40K (sometimes 4K) box. We have two sources for this, conduction, and black body radiation. The focus of this post is reducing the black body load.

Expected Heat load

To calculate the black body head load.

Model: Blank ideal vac wall BB.webp

Heat load from single blank wall


```python

# Radiative heat transfer black body

# Emissivities from Ekin Appendix A2.2
em_Al_polished = 0.03
em_Al_oxidized = 0.3
em_Cu_polished = 0.02
em_Cu_oxidized = 0.6
em_brass_polished = 0.03
em_brass_oxidized = 0.6
em_stainless = 0.07

# Parallel plate surface area (in m^2)
area = 0.031555

# Temperatures + emissiviities of each plate
T2 = 300
emissivity2 = em_Al_polished
T1 = 40
emissivity1 = em_Al_oxidized

# Combined emissivity from Ekin p56
emissivity = emissivity1*emissivity2/(emissivity1+emissivity2-emissivity1*emissivity2)
power = abs(5.67e-8*emissivity*area*(T2**4-T1**4))
print(f'Radiative power = {round(power,3)} W / {round(power*1e3,3)} mW / {round(power*1e6,3)} uW')

Radiative power = 0.406 W / 406.197 mW / 406196.764 uW per blank wall

Adding multiple PCB layers

Area is of 40K black body PCB layer

# Computing effectiveness of multilayer insulation
 
 
import numpy as np
from scipy.optimize import fsolve
 
 
Tfirst = 300
Tlast = 40
N = 8 # Number of mylar layers
emissivity_first = 0.1 # Emissivity of the first layer (e.g. 300K walls)
emissivity_mylar = 0.1 # Emissivity of the multilayer mylar layers
emissivity_last = 0.09 # Emissivity of the last layer (e.g. 40K walls)
 
area = 0.017609 # In m^2
 
def multilayer_insulation_balance_eqns(x):
    """ Sets up equations of the form σEA(T_2^4 - T_1^4) - qdot = 0 for nonlinear solving """
 
    T = np.concatenate([[Tfirst], x[:-1], [Tlast]])
    eps = [emissivity_first] + [emissivity_mylar]*(len(T)-2) + [emissivity_last]
    qdot = x[-1]
    eqns = []
    for n in range(len(T)-1):
        sigma = 5.67e-8 # Stefan-Boltzmann constant
        eps1 = eps[n+1]
        eps2 = eps[n]
        E = eps1*eps2/(eps1+eps2-eps1*eps2)
        A = area
        eqn = sigma*E*A*(T[n+1]**4-T[n]**4) - qdot
        eqns.append(eqn)
    return np.array(eqns)
 
 
T_guess = np.linspace(Tfirst, Tlast, N+2)[1:-1]
qdot_guess = 0.1
x0 = np.concatenate([T_guess, [qdot_guess]])
 
xsolve = fsolve(multilayer_insulation_balance_eqns, x0)
qdot = xsolve[-1]
Tlayers = xsolve[:-1]
print(f'Layer temperatures : {Tlayers}')
print(f'Thermal power : {abs(qdot)}')
# print(f'Error: {multilayer_insulation_balance_eqns(xsolve)}')
 
Layer temperatures : [ 291.35666865  281.86745894  271.30970521  259.35197413  245.46554169
  228.71840805 -207.18613682  175.5040256 ]
Thermal power : 0.04697389608514397

Hardware & Files Required:

Hardware Totals:

  • 40K and 4K walls/layers
    • 48 x 4-40 1/2” SS screw 92196A110
    • 48 x 18-8 Stainless Steel Nylon-Insert Locknut 4-40 91831A005
    • 176 x #4 Nylon washer 90295A363
  • Idealvac Walls (Total walls on cube is 8, 1 x 4KF40, 1 x KF50, 6 x Blanks ) 7 in which we apply BB shielding
    • 28 x 1/4-20 3/8” Nylon screw 95868A735
    • 140 x 1/4” Nylon washer 95606A430

PCB Ordering

  • Top 40K Wall
    • Layers: 2
    • PCB QTY: 4 ( must choose “5”)
    • Surface finish: Leadfree HASL
    • PCB Thickness: 0.8mm
  • Top 40K shield/layer
    • Layers: 4
    • PCB QTY: 8 (must choose “10”)
    • Surface finish: Leadfree HASL
    • PCB Thickness: 0.8mm
  • Bottom 40K Wall
    • Layers: 2
    • PCB QTY: 4 ( must choose “5”)
    • Surface finish: Leadfree HASL
    • PCB Thickness: 0.8mm
  • Bottom 40K shield/layer
    • Layers: 4
    • PCB QTY: 16 (must choose “20”)
    • Surface finish: Leadfree HASL
    • PCB Thickness: 0.8mm
  • IdealVac Walls
    • Layers: 4
    • PCB QTY: 7 walls * 4 layers = 28 (must choose “30”)
    • Surface finish: Leadfree HASL
    • PCB Thickness: 0.8mm
  • 4K Wall
    • Layers: 2
    • PCB QTY: 4 ( must choose “5”)
    • Surface finish: Leadfree HASL
    • PCB Thickness: 0.8mm
  • 4K shield/layer
    • Layers: 4
    • PCB QTY: 8 (must choose “10”)
    • Surface finish: Leadfree HASL
    • PCB Thickness: 0.8mm

TODO:
4K walls are hitting 40K bar stock.

  • Reduce width ~2-3mm
  • Increase shield 4-40 hole clearance
    Bottom 40K walls are difficult to install without pushing 4th layer in so clear cube frame
  • Reduce height and width by ~ 1-3mm
  • increase shield 4-40 clearance holes
    Top 40K walls hit cube connecting o-ring centering ring. The CAD model now includes this.
  • Reduce top 40K shield layers to 1
  • Reduce width on bottom of top 40K shield so it doesn’t interfere with cube centering o-ring.
    • increase shield 4-40 clearance holes

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