South Atlantic Anomaly definition

A. Contin1), D. Grandi2)

1) University of Bologna and INFN, Bologna, Italy

2) INFN, Milano Bicocca, Italy

19 June 2012

1 Introduction

The very high rate of particles in the South Atlantic Anomaly (SAA) region, due to the local decrease of theEarth magnetic field, saturates the AMS-02 data acquisition. It is therefore mandatory to exclude the regionfrom the data analysis.

A good definition of the SAA region is needed for an homogenous and coherent data analysis, taking intoaccount that the exclusion of the SAA region subtracts to the experiment total exposure, so it has to be aslimited as possible.

In the following, the definition of the SAA contour is done in terms of:

• live time of AMS data acquisition system, as a proxy for the total trigger rate on the detector;

• absolute particle rate on the first plane of the TOF system;

• Earth magnetic field.

The following analysis has been done using data collected from May 19 to December 20, 2012 reconstructedwith the B550 reconstruction program version.

2 Experiment live time

The experiment live time is computed through the ratio between two onboard scalers, one which counts the fasttrigger (FT) rate when the DAQ is active (i.e., not busy), and the other which counts the total FT rate. Theresult is shown in Fig. 1 as a function of the geographic coordinates. A cut:

live time < 0.65 (1)

defines the white region in Fig. 2.The total exposure time loss due to cut (1) is 3.2%.

3 Absolute rate on the first TOF plane

The TOF time signals and the Fast Trigger are registered on pipeline TDCs. In particular:

• all Low Threshold (LT) signals are registered in individual channels;

• the Fast Trigger (FT) signal is registered in one channel in each SFET card.

The pipelines length is 655,360 channels at 24.2 ps/ch, for a total of 15, 860 ns. The pipelines are frozen by theLVL1 trigger. As there is a nearly fixed delay between LVL1 and FT, the FT signal is typically in the middleof the pipeline (see Fig. 3). The LT signals distribution is shown in Fig. 4. Off-time events, i.e. events not incoincidence with a trigger, can be clearly identified as the background before and after the triggered events.

A fiducial region from 0 to 200,000 TDC channels can be defined to look for ”off-time events”, defined as acoincidence of LTs between the two sides of a counter. The time difference between the two sides of a counter

1

is shown in Fig. 5a for triggered events and in Fig. 5b for off-time events. The two peaks structure is due tothe different time offsets in the different layers. As the two distributions are very similar, we are confident thata coincidence of off-time LT signals in the two sides represents a real particle hitting the counter.

Each analyzed event contribute to the live time of the off-time events with 200, 000× 0.0242 = 4840 ns. Thetotal rate in each counter can thus be computed by counting the off-time events in that counter and dividingby the total live time for off-time events.

Figure 6 shows the rate of hits in any of the counters in the first TOF layer as a function of the geographiccoordinates. A cut:

rate > 2× 104Hz (2)

defines the white region in Fig. 7.The total exposure time loss due to cut (2) is 3.5%.

4 Earth magnetic field

The Earth has a magnetic field, also known as the geomagnetic field, that extends from the Earth’s inner coreto where it meets the solar wind. It can be approximated with a magnetic dipole tilted at an angle of ≃11o

with respect to the rotational axis and shifted from the Earth center.The Earth’s field changes over time and it is most probably generated by the motion of charged ions (iron)

in the Earth’s outer core.The International Geomagnetic Reference Field (IGRF) is a standard mathematical description of the Earth’s

main magnetic field widely used in studies also for the Earth’s magnetosphere.In source-free regions at the Earth’s surface and above, the main field, with sources internal to the Earth,

is the negative gradient of a scalar potential V which can be represented by a truncated series of sphericalharmonic expansion coefficients.

These IGRF model coefficients are obtained using magnetic field data from satellites and from observatoriesand surveys around the world.

The Earth magnetic field computed with the last IGRF model (IGRF-11) at an altitude of 400 km from thesurface is shown in Fig. 8 as a function of the geographic coordinates.

A cut:

B < 2.15× 10−5T (3)

defines the white region in Fig. 9.We evaluated also the variation of the above mentioned region with altitude, in the range of the ISS motion

(down to a minumim of 340 km), and we found that the main differences where below 0.003 × 10−5T, so thisessentially do not affect the magnetic definition of this region.

The total exposure time loss due to cut (3) is 4.4%.

5 Conclusions

Figure 10 show the comparison between cuts (1), (2) and (3) for the identification of the SAA. All three regionsare completely superimposed.

A simpler solution is to apply a poligonally-shaped cut, as shown in Fig. 11. The coordinates of the pointsA to E can be written as:

• A=(-83-α,-1)

• B=(-38+α,-1)

• C=(0+0.35α,-22)

• D=(0+α,-60)

• E=(-83-α,-60)

with a free parameter α which determines the width of the poligon in the longitude coordinate.Figure 12 shows the data taking time loss as a function of parameter α. A value α between 0 and 10 seems

to be a good compromise, as shown in Fig. 13, giving a total reduction in the exposure time of 11-14%.

2

In Appendix A the code for implementing the cut is given.

3

A Code to implement the cut on an event by event basis

bool pnpoly(int npol, float *xp, float *yp, float x, float y){

int i, j;

bool c=false;

for (i = 0, j = npol-1; i < npol; j = i++) {

if ((((yp[i] <= y) && (y < yp[j])) ||

((yp[j] <= y) && (y < yp[i]))) &&

(x < (xp[j] - xp[i]) * (y - yp[i]) / (yp[j] - yp[i]) + xp[i]))

c = !c;

}

return c;

}

....

AMSEventR *pev;

float alpha=0;

float Phi_SAA[5] = {-83.-alpha, -38.+0.35*alpha, 0.+alpha, 0.+alpha, -83.-alpha};

float Theta_SAA[5] = {-1., -1., -22., -60., -60.};

double pigr=acos(-1.);

. ... event loop ....

HeaderR* header = &(pev->fHeader);

float ThetaS = header->ThetaS*180./pigr;

float PhiS = header->PhiS*180./pigr;

if(PhiS>180 && PhiS<360) PhiS = -360+PhiS;

bool in_SAA = pnpoly(5, Phi_SAA, Theta_SAA, PhiS, ThetaS);

if( !in_SAA ){

.... event analysis ...

}

4

Phi-150 -100 -50 0 50 100 150

Th

eta

-80

-60

-40

-20

0

20

40

60

80 29.29

0 88 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure 1: Fraction of live time as a function of the geographic coordinates.

Phi-150 -100 -50 0 50 100 150

Th

eta

-80

-60

-40

-20

0

20

40

60

80

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure 2: Fraction of live time as a function of the geographic coordinates. The white region corresponds tolive time < 0.65.

5

FT (TDC ch.)0 100 200 300 400 500 600

310×

even

ts/1

000

TD

C c

h.

210

310

410

510

610

Figure 3: Time distribution of the FT signals.

LT (TDC ch.)0 100 200 300 400 500 600

310×

even

ts/1

000

TD

C c

h.

310

410

510

610

Figure 4: Time distribution of the LT signals.

6

LTp-LTn (ns)-500 -400 -300 -200 -100 0 100 200 300 400 500

even

ts/2

ns

310

410

510

610

LTp-LTn (ns)-500 -400 -300 -200 -100 0 100 200 300 400 500

even

ts/2

ns

1

10

210

a) b)

Figure 5: Time distribution of the difference between the LT signals from the two sides of a counter for (a)triggered events and (b) off-time events. The two peaks correspond to different planes.

Phi-150 -100 -50 0 50 100 150

Th

eta

-80

-60

-40

-20

0

20

40

60

80

1

10

210

310

410

510

Figure 6: Particle rate (Hz) on the first TOF layer as a function of the geographic coordinates.

7

Phi-150 -100 -50 0 50 100 150

Th

eta

-80

-60

-40

-20

0

20

40

60

80

1

10

210

310

410

Figure 7: Particle rate (Hz) on the first TOF layer as a function of the geographic coordinates. The whiteregion corresponds to a rate > 2× 104Hz.

Phi-150 -100 -50 0 50 100 150

Th

eta

-80

-60

-40

-20

0

20

40

60

80

0

0.01

0.02

0.03

0.04

0.05

-310×

Figure 8: Magnetic field (T) isolines as a function of the geographic coordinates.

8

Phi-150 -100 -50 0 50 100 150

Th

eta

-80

-60

-40

-20

0

20

40

60

80

0

0.01

0.02

0.03

0.04

0.05

-310×

Figure 9: Magnetic field (T) isolines as a function of the geographic coordinates.The white region correspondsto B < 2.15× 10−5T.

Phi-150 -100 -50 0 50 100 150

Th

eta

-80

-60

-40

-20

0

20

40

60

80

Figure 10: SAA definition with the three methods: fraction of live time (blue line), rate (red line), magneticfield (green line).

9

Phi-150 -100 -50 0 50 100 150

Th

eta

-80

-60

-40

-20

0

20

40

60

80

A

E

B

C

D

Figure 11: SAA definition with a poligon, superimposed to the plot of Fig. 10. The dashed lines represent thelatitude limits of the ISS orbit.

0 5 10 15

expo

sure

loss

200

5%

10%

15%

20%

αFigure 12: The loss in AMS-02 exposure time as a function of the parameter α defined in the text.

10

Phi-150 -100 -50 0 50 100 150

Th

eta

-80

-60

-40

-20

0

20

40

60

80

1

10

210

310

410

A'

E'

A

E

B'B

C'

D'

C

D

Figure 13: SAA definition with a poligon, superimposed to the plot of Fig. 6 (rate), using a value of α of 0(solid lne) and 10 (dashed line), as explained in the text.

11