TES-Simulations

Jörn Wilms (FAU), P. Peille (IRAP), M. Ceballos (IFCA), T. Brand (ECAP),T. Dauser (ECAP), S.J. Smith (GSFC), B. Cobo (IFCA), S. Bandler (GSFC),

R. den Hartog (SRON), J. de Plaa (SRON), E. Pointecouteau (IRAP),D. Barret (IRAP)

Simulation ansatz 1

X-IFU photon detection process:• sensitivity described by effective area curves

(taking into account mirror reflectivity, pixel sensitivity, gaps)

• Two (input/output-compatible) simulation approaches– xifupipeline:∗ full imaging implemented∗ fast detection simulation using response matrices=⇒Well suited for faint sources

– tessim/sirena∗ Simulation of TES physics and pulse reconstruction∗ Slower than xifupipeline, but much better physics=⇒Well suited for bright sources=⇒Well suited for engineering studies

Will soon be able to easily switch simulation between both

Simulation ansatz 2

Device Simulations: Principle

Smith (2006 PhD Leicester)

Calorimeter: measure temperature change in device with temperature T0 connected to heat bathwith temperature TS.Joule heating by current through device =⇒ T0 > TS

Absorption: temperature rises: ∆T = Eγ/CC: heat capacity

Relaxes back to T0. Typical timescale: τ = C/G.Resolution given by thermal fluctuations: ∆E = 2.35

√kT 2C

=⇒ Small (few eV) for T small (mK)

Simulation ansatz 3

Device Simulations: Principle

Kinnunen (2011, PhD Jyväskylä)negative electrotermal feedback: Oper-ate circuit at Transition Edge betweensuperconduction and normal conduction,voltage bias circuit:absorption =⇒ R ↗=⇒ Joule power PJ = I2R ↘=⇒ faster cooling than for R = constTypical time constants 75µs. . . 400µs

X-IFU Simulation 1

Tessim

1.00.80.60.40.20.0-0.2

0.030

0.025

0.020

0.015

0.010

0.005

0.000

Time since photon impact [ms]

Pulsesh

apenorm

alized

toequalarea

10.0 keV5.0 keV3.0 keV2.0 keV1.0 keV0.1 keV

1.00.80.60.40.20.0-0.2

1.0

0.9

0.8

0.7

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0.5

0.4

0.3

0.2

0.1

0.0

Time since photon impact [ms]

Pulsesh

apenorm

alized

topeak

10.0 keV5.0 keV3.0 keV2.0 keV1.0 keV0.1 keV

SLA pulse shapes for 0.1, 1, 2, 3, 5,10 keV, normalized to top: equal area,bottom: peak current.

• based on GSFC code by S.J. Smith• numerical solution of differential equa-

tions for T (t), I(t) (e.g., Irwin & Hilton,2005),

CdTdt

= −Pb + PJ + P + Noise

LdIdt

= V − IRL − IR(T , I) + Noise

• linear resistance model, R(T , I;α, β)• noise treatment: Johnson of circuit, bath,

excess noise• input parameters: C, Gb, n, α, β, m, R0,

T0, Tb, Lcrit

including flexible, FITS-based library of pixel types

X-IFU Simulation 2

Tessim

1.00.80.60.40.20.0-0.2

0.030

0.025

0.020

0.015

0.010

0.005

0.000

Time since photon impact [ms]

Pulsesh

apenorm

alized

toequalarea

10.0 keV5.0 keV3.0 keV2.0 keV1.0 keV0.1 keV

1.00.80.60.40.20.0-0.2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Time since photon impact [ms]

Pulsesh

apenorm

alized

topeak

10.0 keV5.0 keV3.0 keV2.0 keV1.0 keV0.1 keV

SLA pulse shapes for 0.1, 1, 2, 3, 5,10 keV, normalized to top: equal area,bottom: peak current.

• based on GSFC code by S.J. Smith• numerical solution of differential equa-

tions for T (t), I(t) (e.g., Irwin & Hilton,2005),

CdTdt

= −Pb + PJ + P + Noise

LdIdt

= V − IRL − IR(T , I) + Noise

• linear resistance model, R(T , I;α, β)• noise treatment: Johnson of circuit, bath,

excess noise• input parameters: C, Gb, n, α, β, m, R0,

T0, Tb, Lcrit

including flexible, FITS-based library of pixel types

Linear Resistance Model:

R(T , I) = R0 +∂R∂T

∣∣∣∣I0

(T − T0) +∂R∂I

∣∣∣∣T0

(I − I0) (1)

where

α =∂ log R∂ log T

∣∣∣∣I0

=T0

R0

∂R∂T

∣∣∣∣I0

(2)

β =∂ log R∂ log I

∣∣∣∣T0

=I0R0

∂R∂I

∣∣∣∣T0

(3)

more complicated resistance models are to be implemented(BSc work Christian Kirsch)

X-IFU Simulation 3

Tessim

1.00.80.60.40.20.0-0.2

0.030

0.025

0.020

0.015

0.010

0.005

0.000

Time since photon impact [ms]

Pulsesh

apenorm

alized

toequalarea

10.0 keV5.0 keV3.0 keV2.0 keV1.0 keV0.1 keV

1.00.80.60.40.20.0-0.2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Time since photon impact [ms]

Pulsesh

apenorm

alized

topeak

10.0 keV5.0 keV3.0 keV2.0 keV1.0 keV0.1 keV

SLA pulse shapes for 0.1, 1, 2, 3, 5,10 keV, normalized to top: equal area,bottom: peak current.

• based on GSFC code by S.J. Smith• numerical solution of differential equa-

tions for T (t), I(t) (e.g., Irwin & Hilton,2005),

CdTdt

= −Pb + PJ + P + Noise

LdIdt

= V − IRL − IR(T , I) + Noise

• linear resistance model, R(T , I;α, β)• noise treatment: Johnson of circuit, bath,

excess noise• input parameters: C, Gb, n, α, β, m, R0,

T0, Tb, Lcrit

including flexible, FITS-based library of pixel types

Noise terms:

• Johnson noise in the TES

• Johnson noise in the load resistor

• Thermal fluctuation noise

• Excess noise

see Irwin & Hilton (2005) for detailsrequires special care in numerical integrator

tessim 1

tessim

Translation to program: (too) many parameters ;-)

tessim 2

Configuration controlSolution to large number of parameter problem:self documentation =⇒ store all parameters in FITS files output by tessim: canreload exact pixel configuration from any stream produced by tessim:

First run tessim with propertiesonly=yes:

tessim PixType=LPA1 Ce=0.26 Gb=280 ... propertiesonly=yes... Streamfile=testpixel.fits

Later run with

tessim PixType=file:testpixel.fits[LPA1]Streamfile=simulation PixImpList=impact.fits

where ...[LPA1]: FITS selection syntax on FITS HDUNAME keyword.impact.fits

: FITS impact file with TIME and ENERGY columns.

tessim 3

Trigger

EventDetection

EventGrading

UncalibratedE

Energy

Iterative Event Detection (Triggering):

• Take derivative of TES streamtrigger=

– stream– movavg:npts:threshold:suppress– diff:npts:threshold:suppress

• remove pulses on the go to findothers

0.1040.1020.1000.0980.096

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1.6

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0.1040.1020.1000.0980.096

Time [s]

Current[µ

A]

tessim 4

Trigger

EventDetection

EventGrading

UncalibratedE

Energy

Iterative Event Detection (Triggering):

• Take derivative of TES streamtrigger=

– stream– movavg:npts:threshold:suppress– diff:npts:threshold:suppress

• remove pulses on the go to findothers

0.1040.1020.1000.0980.096

1.7

1.6

1.5

1.4

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100

80

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40

20

0

-20

Time [s]

Current[µ

A]

Deriv

ativ

edI/dt[µ

A/sample]

tessim 5

Trigger

EventDetection

EventGrading

UncalibratedE

Energy

Event Grading: Resolution depends on distance between different pulses.

tessim 6

Trigger

EventDetection

EventGrading

UncalibratedE

Energy

Energy calculation: Use optimal filter(Szymkowiak et al., 1993):

E ∝∑ D(f )S∗(f )

N(f )where• D(f ): data spectrum,• S(f ): template spectrum,• N(f ): noise spectrum

Caveats:• exact degradation at higher

energies not yet studied fortime reasons• reconstruction algorithms

still in development and un-der optimization, have donefirst studies using principlecomponent analysis andresistance space optimalfiltering