^{1,2}, Z. Sternovsky

^{1,3}, E. Grün

^{1}, S. Auer

^{4}, N. Duncan

^{1}, K. Drake

^{1}, H. Le

^{1}, M. Horanyi

^{1,2}and R. Srama

^{5,6}

### Abstract

The Dust Trajectory Sensor (DTS) instrument is developed for the measurement of the velocity vector of cosmic dust particles. The trajectory information is imperative in determining the particles’ origin and distinguishing dust particles from different sources. The velocity vector also reveals information on the history of interaction between the charged dust particle and the magnetospheric or interplanetary space environment. The DTS operational principle is based on measuring the induced charge from the dust on an array of wire electrodes. In recent work, the DTS geometry has been optimized [S. Auer, E. Grün, S. Kempf, R. Srama, A. Srowig, Z. Sternovsky, and V Tschernjawski, Rev. Sci. Instrum.79, 084501 (2008)10.1063/1.2960566] and a method of triggering was developed [S. Auer, G. Lawrence, E. Grün, H. Henkel, S. Kempf, R. Srama, and Z. Sternovsky, Nucl. Instrum. Methods Phys. Res. A622, 74 (2010)10.1016/j.nima.2010.06.091]. This article presents the method of analyzing the DTS data and results from a parametric study on the accuracy of the measurements. A laboratory version of the DTS has been constructed and tested with particles in the velocity range of 2–5 km/s using the Heidelberg dust accelerator facility. Both the numerical study and the analyzed experimental data show that the accuracy of the DTS instrument is better than about 1% in velocity and 1° in direction.

The presented work was supported by the National Aeronautics and Space Administration (NASA) and by internal funds from the Laboratory of Atmospheric and Space Physics (LASP) of the University of Colorado.

I. INTRODUCTION

II. DUST TRAJECTORY SENSOR

III. DTS NUMERICAL MODELING

IV. ANALYSIS OF THE DTS MEASUREMENTS

V. SENSITIVITY AND ACCURACY OF THE DTS

VI. LABORATORY TESTING OF THE DTS PROTOTYPE AND DATA ANALYSIS

VII. SUMMARY AND CONCLUSIONS

### Key Topics

- Electrodes
- 72.0
- Interplanetary dust
- 32.0
- Data analysis
- 21.0
- Numerical modeling
- 13.0
- Electronic devices
- 11.0

## Figures

The schematic of the DTS. Each wire electrode is connected to a separate CSA. The entrance and exit grids are part of the shielding Faraday box around the array of electrodes.

The schematic of the DTS. Each wire electrode is connected to a separate CSA. The entrance and exit grids are part of the shielding Faraday box around the array of electrodes.

The COULOMB model of the DTS. There are four electrode planes with seven wires in each. The wires in planes 1 and 3 are along the *y*-axis and wires in planes 2 and 4 are along the *x*-axis. The origin of the coordinate system is placed at the center of the box. The kernel volume is shown in the middle and the dimensions are given in mm.

The COULOMB model of the DTS. There are four electrode planes with seven wires in each. The wires in planes 1 and 3 are along the *y*-axis and wires in planes 2 and 4 are along the *x*-axis. The origin of the coordinate system is placed at the center of the box. The kernel volume is shown in the middle and the dimensions are given in mm.

The effect of the proximity of the wall on charge (*Q* _{3, 5}) induced on the closest wire that is located at *x* = 0 mm, *y*, *z* = −20 mm. The figure shows the induced charge as a function of the distance from the wall for a few different fixed *x* and *z* coordinates. The effect of the wall is the strongest, when the dust particle is in between two electrode planes (*z* = 0 mm). The bottom panel shows the induced charge relative to the undisturbed kernel results.

The effect of the proximity of the wall on charge (*Q* _{3, 5}) induced on the closest wire that is located at *x* = 0 mm, *y*, *z* = −20 mm. The figure shows the induced charge as a function of the distance from the wall for a few different fixed *x* and *z* coordinates. The effect of the wall is the strongest, when the dust particle is in between two electrode planes (*z* = 0 mm). The bottom panel shows the induced charge relative to the undisturbed kernel results.

The effect of the entrance grid and the shape of the correction function *f* (*z* _{ p }). The figure shows the induced charge on the nearest electrode as a function of distance, with and without the wall effect included. The ratio of the two calculations defines the shape of the correction function *f* (*z* _{ p }).

The effect of the entrance grid and the shape of the correction function *f* (*z* _{ p }). The figure shows the induced charge on the nearest electrode as a function of distance, with and without the wall effect included. The ratio of the two calculations defines the shape of the correction function *f* (*z* _{ p }).

Simulated induced charge signals from a dust particles with incidence angles *θ* _{ x } = −5.7° and *θ* _{ y } = 16.8°. The signals from the four closest wire electrodes in each plane are shown. The data are normalized to the dust charge, and the curves are staggered in the vertical direction for clarity. The vertical lines mark the positions of the four electrode planes.

Simulated induced charge signals from a dust particles with incidence angles *θ* _{ x } = −5.7° and *θ* _{ y } = 16.8°. The signals from the four closest wire electrodes in each plane are shown. The data are normalized to the dust charge, and the curves are staggered in the vertical direction for clarity. The vertical lines mark the positions of the four electrode planes.

The effect of the limited size DTS model on the induced charge. The figure shows the induced charge on the closest electrode (*Q* _{3, 5}) as the particles moved between points (10, 10, −20) and (10, 10, 0). The model with 7 wire electrodes in each plane yields somewhat smaller induced charge signals. The bottom panel shows the ratio of the signals from the two models.

The effect of the limited size DTS model on the induced charge. The figure shows the induced charge on the closest electrode (*Q* _{3, 5}) as the particles moved between points (10, 10, −20) and (10, 10, 0). The model with 7 wire electrodes in each plane yields somewhat smaller induced charge signals. The bottom panel shows the ratio of the signals from the two models.

The convergence of the χ^{2}-minimum with increasing number of iteration steps. The different lines correspond to different data analysis runs. The simulated signal is for a 5.21 km/s velocity particle with added white noise (QNR = 10), see Sec. V for details. The dust particle moves from point (−5.5, −10, −100) to point (32, −10, 100), which corresponds to *θ* _{ x } = 10.62° and *θ* _{ y } = 0°.

The convergence of the χ^{2}-minimum with increasing number of iteration steps. The different lines correspond to different data analysis runs. The simulated signal is for a 5.21 km/s velocity particle with added white noise (QNR = 10), see Sec. V for details. The dust particle moves from point (−5.5, −10, −100) to point (32, −10, 100), which corresponds to *θ* _{ x } = 10.62° and *θ* _{ y } = 0°.

Uncertainty of the parameters determined from the analysis as a function of QNR. The two outliner points (diamond and cross) are discussed in details in the text.

Uncertainty of the parameters determined from the analysis as a function of QNR. The two outliner points (diamond and cross) are discussed in details in the text.

The schematics of the charge sensitive electronics (CSA) integrated into the laboratory version.

The schematics of the charge sensitive electronics (CSA) integrated into the laboratory version.

An example of the DTS data and the best fit provided by the analysis (thick smooth lines). Signals from the eight electrodes closest to the path of the dust particle are shown. The calculated particle parameters are: Q = 15.77 fC, v = 4.57 km/s, *θ* _{ x } = 0.086°, and *θ* _{ y } = 0.98°. The curves are staggered in the vertical direction for clarity.

An example of the DTS data and the best fit provided by the analysis (thick smooth lines). Signals from the eight electrodes closest to the path of the dust particle are shown. The calculated particle parameters are: Q = 15.77 fC, v = 4.57 km/s, *θ* _{ x } = 0.086°, and *θ* _{ y } = 0.98°. The curves are staggered in the vertical direction for clarity.

Results of the analyses of the data for 0° and 10° incident angles. The panels show the (a) charge, (b) speed, (c) incident angle θ_{ x }, and (d) incident angle θ_{ y }. The shaded areas indicate +/−1° deviations from the mean value (outliner points excluded).

Results of the analyses of the data for 0° and 10° incident angles. The panels show the (a) charge, (b) speed, (c) incident angle θ_{ x }, and (d) incident angle θ_{ y }. The shaded areas indicate +/−1° deviations from the mean value (outliner points excluded).

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