BLOCK

SHELL

SHIELDS

A lumped thermal model of the STAR enclosure

Model: • thermal input is applied to the shell • thermal couplings include radiation and conduction • radiation approximated as linear in del-T • thermal couplings all equal (for now) • shields have equal heat capacities - Al • block has heat capacity of 1000 cc glass • temperatures referenced to T=0 starting condition • no gradients except between stages • shields numbered from the outside in

2.0

1.5

1.0

0.5

0.0

-0.5

-1.0

TEM

PER

ATU

RE

OFF

SET,

deg

rees

10008006004002000TIME, arb. units

shell temp first shield second shield x100 third shield x100fourth shield x100 fifth shield x100 block x1000

Generic lumped thermal model analysis: Thermal response of all layers (note scale factors in box) Excitation: sine wave on outer shell starting at t = 0

2.0

1.5

1.0

0.5

0.0

-0.5

-1.0500040003000200010000

Behavior on a longer time scale:

1.0605

1.0600

1.0595

1.0590

1.0585

135013001250

~ 50 nanodegrees

block x 1000, scale at left is: 500 nano-deg/division

Magnifying the behavior of the block near the maximum offset:

1.0606405

1.0606400

1.0606395

1.0606390

1.0606385

1.0606380

1301.01300.51300.01299.51299.0

~ 0.05 nanodegrees

block x 1000, scale at left is: 0.5 nano-deg/division

Discretization of the computation:

1.0

0.5

0.0

-0.5

-1.010008006004002000

Let’s add a servo to the first shield: just a proportional servo, gain not optimized

30

20

10

0

-10

-20

x10-3

1000950900850

Looking more closely at the ‘final’ state with the servo:

25.96

25.94

25.92

25.90

25.88

25.86

25.84

25.82

x10-3

980960940920900880860840

~ 50 nanodegrees

The behavior of the block near the maximum: (remember it is x1000)

25.96

25.94

25.92

25.90

25.88

25.86

25.84

25.82

x10-3

980960940920900880860840

Block behavior with 10 micro-degree sigma random noise added to the servo input: - program updates once per second

Conclusions from generic case:

• lumped model provides insight to overall behavior • sub-nanokelvin resolution is easy to achieve • startup transients are associated with phase lags • lumped results can be obtained quickly • servo implementation just requires the control law • outer stage servo is effective in suppressing transients • effects of servo noise can easily be evaluated • need to get quantitative parameters for quantitative results • useful for predicting behavior of hardware experiment • computation speed/memory not issues for lumped model • detailed gradient issues are more easily addressed in Comsol

Response of all stages to a 1-degree temperature step on the shell:

First look at model with ‘real’ parameter values from Joey, Using sine wave excitation at orbital period: - estimated attenuation: 3x108

Magnified behavior of the block near the maximum:

Replacing the sine wave excitation with Joey’s data for the shell temperature variation in an equatorial orbit:

Detailed view of first few cycles:

Conclusions for baseline design:

• very good passive filtering of orbital period: - see << 1 nanodegree pp @ orbital - 2007 design gave ~ 5 microdegrees pp @ orbital - passive design now exceeds KT requirements even for equatorial orbit • improved design and analysis realism over 2007 proposal has improved passive lumped performance significantly • block-to-shell relaxation time is multi-days • need to refine parameter values to match hardware better • need to quantify thermal gradient issues further

More realistic servos: Add a servo to outer shield: - simple proportional controller -starts when shield is at 0.1 K offset, moves to 0.4 K offset

Move the servo to the inner shield, same gain and trigger:

Reducing the servo gain by a factor of 50:

Teamwork: the art of working together

Joey: thanks for your help!