# Design and Optimization of a High-Time-Resolution Magnetic Plasma Analyzer (MPA)

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## Abstract

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## Featured Application

**This instrument concept is designed to analyze plasma onboard scientific spacecraft. Its measurements allow the construction of the velocity distribution functions of protons and $\mathit{\alpha}$-particles with high cadence to understand the small-scale kinetic processes in space plasmas.**

## Abstract

## 1. Introduction

#### 1.1. Scientific Objectives

#### 1.2. State-of-the-Art Space Plasma Instruments

#### 1.3. Instrument Working Principle and Expectations

## 2. Instrument Design

#### 2.1. Instrument Geometry and Functionning

#### 2.2. Position of the Sensor to Obtain Optimal Velocity Resolution

#### 2.3. Dependence of the Field of View on Speed and Determination of the Magnetic Chamber Width

#### 2.4. From Counts to a VDF

#### 2.5. Instrument Length

#### 2.6. Summarized Instrument Geometry

## 3. Instrument Performance

#### 3.1. Velocity Resolution

#### 3.2. Errors Based on Counting Statistics

#### 3.3. Optimization of the Aperture Size, Pixel Size, and Magnetic Field Strength

## 4. Instrument Simulation

#### 4.1. SIMION Results for Protons

#### 4.2. SIMION Results for Combined Proton and $\alpha $-Particle Measurements

## 5. Discussion and Conclusions

#### 5.1. Magnetic Field Design

#### 5.2. Detectors and Readout Electronics

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Basic geometry of MPA. The instrument model has a conical aperture of diameter a at the entrance of the magnetic chamber (yellow area) with a semi angle of ${2.5}^{\circ}$. In Figure 1b, we represent the trajectories of three ions with equal mass, charge and speed but different offsets from the central aperture axis. (

**a**): Face view; (

**b**): Side view.

**Figure 2.**Variation of the out-of-plane view angle $\gamma $ with velocity for different chamber width. These curves simulate protons flying through the instrument chamber with different gap width (6, 8, 10, 12 and 14 mm), and a magnetic field strength of ${B}_{0}=0.1$ T.

**Figure 3.**Five beams of particles are simulated using the SIMION software. Each beam has a set speed and a cylindrical (uniform) distribution of positions at the aperture of the instrument. The radius of the beam is 1 mm (2-mm disk aperture). Pixels are the areas separated by black horizontal lines.

**Figure 4.**Evolution of the counting errors with particle speed. The top plot shows the $2\sigma $ error bars on the expected counts for each pixel. The bottom plot represents the relative error (${e}_{r}$) in percent made on the determination of the speed. The 10% (green) and 20% (red) levels are represented.

**Figure 5.**Maxwellian VDF with density 5 cm${}^{-3}$, temperature 100,000 K and bulk speed 500 km/s. This distribution function serves as the input for our calculations in Section 3.2.

**Figure 6.**Maxwellian and $\kappa $ VDFs with parameters summarized in Table 3. These distribution functions serve as inputs for the following simulations.

**Figure 7.**Relative errors in percent made on measurements of an intermediate solar wind (bulk speed of 500 km/s, temperature of 100,000 K and density of 5 cm${}^{-3}$) as a function of aperture and pixel size. Panels (

**a**) through (

**g**) show the resulting relative errors for all of the fit parameters of the Maxwellian and $\kappa $-distributions.

**Figure 8.**Relative errors in percent made on an intermediate solar wind with magnetic field and pixel size. Panels (

**a**) through (

**g**) show the resulting relative errors for all of the fit parameters of the Maxwellian and $\kappa $-distributions.

**Figure 9.**Three different types of solar wind simulated with SIMION. We present the number of counts per pixel (1 mm wide) as a function of hit distance on the position-sensitive sensor along the z-axis in our instrument design. In all three examples, the velocities of the simulated particles follow a Maxwellian distribution function.

**Figure 10.**Estimated (red) and model-input (blue) distribution functions. The estimation of the distribution function is based on the counting results shown in Figure 9. In all three examples, the velocities of the simulated particles follow a Maxwellian distribution function.

**Figure 11.**Three different types of solar wind simulated with SIMION. We present the number of counts per pixel (1 mm wide) as a function of hit distance on the position-sensitive sensor along the z-axis in our instrument design. In all three examples, the velocities of the simulated particles follow a $\kappa $-distribution function with $\kappa =3$.

**Figure 12.**Estimated (red) and model-input (blue) distribution functions. The estimation of the distribution function is based on the counting results shown in Figure 11. In all three examples, the velocities of the simulated particles follow a $\kappa $-distribution function with $\kappa =3$.

**Figure 14.**Estimated (red and green) and model-input (blue and black) distribution functions. The estimation of the distribution function is based on the counting results shown in Figure 13.

**Figure 15.**Position-sensitive anodes and a representative pixel. The anodes are represented by the blue lines. They consist of conductive wires that detect the current generated by the electron beams (gray circles) and determine the vertical z position of the beam based on the knowledge of which wire has been hit. A pixel is defined as either a single anode or a collection of multiple anode wires and is represented here as a yellow rectangle. The two permanent magnets, which delimit the magnetic chamber, are represented by the dark rectangles at both sides of the pixels.

Parameter | Low | Medium | High |
---|---|---|---|

Energy range | 20 keV–240 keV | 80 keV–1200 keV | 800 keV–4800 keV |

Magnetic field strength | 0.055 T | 0.16 T | 0.48 T |

Magnetic chamber gap | 7 mm | 7 mm | 12 mm |

Field of view | ${20}^{\circ}\times {10}^{\circ}$ | ${20}^{\circ}\times {10}^{\circ}$ | ${16}^{\circ}\times {19}^{\circ}$ |

Apperture geometry | 2 mm × 5 mm | 2 mm × 5 mm | 10 mm × 5 mm |

Mass | 8.5 kg | 8.5 kg | 8.5 kg |

Parameter | Value |
---|---|

Aperture shape | Cone of half-angle ${2.5}^{\circ}$ |

Aperture entrance | Disk of radius 1 mm |

Magnetic field | Uniform at 0.1 T |

Instrument length | 30 cm |

Instrument height | 15 cm |

Instrument gap width | 14 mm |

Pixel size | 1 mm |

Parameter | Value |
---|---|

Density | 5 cm${}^{-3}$ |

Temperature | 100,000 K |

Bulk speed | 500 km/s |

$\kappa $ | 3 |

Measurement duration | 5 ms |

FOV | ${5}^{\circ}\times {5}^{\circ}$ |

Magnetic field strength | 0.1 T |

**Table 4.**Slow, intermediate and fast solar wind input parameters for the Maxwellian and $\kappa $-distributions of speed used in SIMION simulations.

Solar Wind | Density (cm${}^{-3}$) | Thermal Speed (m/s) | Bulk Speed (km/s) | $\mathit{\kappa}$ |
---|---|---|---|---|

Slow | 5.5 | 36,341 | 400 | 3 |

Intermediate | 5 | 40,631 | 500 | 3 |

Fast | 3 | 57,460 | 700 | 3 |

Solar Wind | Density (cm${}^{-3}$) | Thermal Speed (m/s) | Bulk Speed (m/s) |
---|---|---|---|

Slow | 5.49 $\pm \phantom{\rule{0.166667em}{0ex}}0.027$ | 36,416 $\pm \phantom{\rule{0.166667em}{0ex}}68$ | 400,062 $\pm \phantom{\rule{0.166667em}{0ex}}48$ |

Intermediate | 4.95 $\pm \phantom{\rule{0.166667em}{0ex}}0.023$ | 40,559 $\pm \phantom{\rule{0.166667em}{0ex}}72$ | 499,973 $\pm \phantom{\rule{0.166667em}{0ex}}51$ |

Fast | 2.94 $\pm \phantom{\rule{0.166667em}{0ex}}0.015$ | 57,154 $\pm \phantom{\rule{0.166667em}{0ex}}113$ | 700,029 $\pm \phantom{\rule{0.166667em}{0ex}}80$ |

Solar Wind | Density (cm${}^{-3}$) | Thermal Speed (m/s) | Bulk Speed (m/s) | $\mathit{\kappa}$ |
---|---|---|---|---|

Slow | 5.43 $\pm \phantom{\rule{0.166667em}{0ex}}0.16$ | 34,538 $\pm \phantom{\rule{0.166667em}{0ex}}1468$ | 399,981 $\pm \phantom{\rule{0.166667em}{0ex}}68$ | 3.44 $\pm \phantom{\rule{0.166667em}{0ex}}0.34$ |

Intermediate | 4.99 $\pm \phantom{\rule{0.166667em}{0ex}}0.2$ | 39,447 $\pm \phantom{\rule{0.166667em}{0ex}}2361$ | 499,994 $\pm \phantom{\rule{0.166667em}{0ex}}101$ | 3.26 $\pm \phantom{\rule{0.166667em}{0ex}}0.41$ |

Fast | 2.96 $\pm \phantom{\rule{0.166667em}{0ex}}0.12$ | 56,492 $\pm \phantom{\rule{0.166667em}{0ex}}3533$ | 699,963 $\pm \phantom{\rule{0.166667em}{0ex}}138$ | 3.10 $\pm \phantom{\rule{0.166667em}{0ex}}0.37$ |

Particle Species | Density (cm${}^{-3}$) | Thermal Speed (m/s) | Bulk Speed (km/s) |
---|---|---|---|

$\alpha $-particles | 0.175 | 24,881 | 500 |

Protons | 4.825 | 40,631 | 500 |

**Table 8.**Estimation of the plasma moments after a least square fitting for the simulated $\alpha $-particles and comparison with the corresponding input values.

Parameter | Input Value | Output Value |
---|---|---|

Density | 0.175 cm${}^{-3}$ | 0.160 cm${}^{-3}$ ± 0.0043 cm${}^{-3}$ |

Thermal speed | 24,881 m/s | 24,151 m/s ± 249 m/s |

Bulk speed | 500 km/s | 496 km/s ± 176 m/s |

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**MDPI and ACS Style**

Criton, B.; Nicolaou, G.; Verscharen, D.
Design and Optimization of a High-Time-Resolution Magnetic Plasma Analyzer (MPA). *Appl. Sci.* **2020**, *10*, 8483.
https://doi.org/10.3390/app10238483

**AMA Style**

Criton B, Nicolaou G, Verscharen D.
Design and Optimization of a High-Time-Resolution Magnetic Plasma Analyzer (MPA). *Applied Sciences*. 2020; 10(23):8483.
https://doi.org/10.3390/app10238483

**Chicago/Turabian Style**

Criton, Benjamin, Georgios Nicolaou, and Daniel Verscharen.
2020. "Design and Optimization of a High-Time-Resolution Magnetic Plasma Analyzer (MPA)" *Applied Sciences* 10, no. 23: 8483.
https://doi.org/10.3390/app10238483