-One-dimensional and two-dimensional axisymmetric models of a dust impact time-of-flight dust particle sensor for analysis of the chemical composition of micrometeoroids and particles of space debris are considered. The results of calculating the design parameters and functional characteristics of the sensor are presented. The algorithm of the program for modelling mass spectra is described. Model mass spectra obtained for the axial case in the one-dimensional approximation, as well as for the two-dimensional case and various coordinates of the impact interaction, are presented. The comparison of model spectra with experimental data obtained at the electrodynamic accelerator of dust particles is given.
Currently, more and more attention is paid to the problem of space debris, which is associated both with an increase in the terms of active existence of spacecrafts, and with an increasing number of anthropogenic origin space debris. Micrometeoroids and anthropogenic dust particles are one of the main factors in outer space, which, along with various emissions and streams of charged particles, cause premature degradation of structural elements of the spacecraft [1, 2], which means that they can lead to a deterioration of its functional characteristics, or failure. Various methods can be used to analyze the properties of dust particle flows, such as aerogel-based traps, non-contact optical measurers, impact ionization sensors [3, 4]. But the greatest amount of information on the physical and chemical properties of a projectile particle can only be obtained by using a massspectrometric type dust impact time-of-flight sensor. Such an analyzer makes it possible to investigate single fast-transient events and evaluate not only the chemical composition of a particle, but also its charge, velocity vector and, indirectly, mass.
The principle of operation of such analyzers [
The principle of the device operation is presented in the ion optical diagram (Fig. 1).
At the initial moment, the dust particle hits the target and
transforms into a cloud of weakly ionized gas, consisting of
ions of the particle material and the target. An electrical
signal is formed during the flight through the detector grid,
along which the recording of a data frame containing
information from the ion receiver begins. Under the
influence of an electric field formed by the potential
difference of the target and the shielding grid, the ion cloud
accelerates in the direction of the ion mirror. The ion mirror
is made in the form of five field-aligning electrodes and four
parabolic grids, the focal point of which coincides with the
receiver of ions. After the turn, the ions enter the receiver
and the signal from the amplifier of the ion receiver enters
the microcontroller module. The design described in [
III. CALCULATION OF THE PARAMETERS OF THE SENSOR A. One-dimensional model
We write an expression that determines the time of flight of a particle of mass m and charge q with an initial energy ∆U: = ( 2 1 1 2 1 ) 1⁄2 {2 1 [√∆ + 1(1 + )− √∆ ] + + 4 3 [√∆ + 1 − √∆ + 1(1 − 1)] + + 4 4 √∆ + 1(1 − 1)+ fl(∆ + 1)−1⁄2.
Further, we write through the coefficients = ( )
[ 1√∆ + 2√∆ + 1 + + 3√∆ + 1(1 − 1)+ 4(∆ + 1)−1⁄2] 1 = − 2 1; 1 2 1 the expression, the term 1√∆ turns into 1( 1√∆ ) after substitution and differentiation. In condition when ∆U tends to zero, the derivative tends to infinity. By tending ∆U to very small values, we obtain a solution that cannot be realized constructively: the sizes L1 and L2 will be very small (L1 tends to zero, and the value of L2 is of the order of −1 mm).
Therefore, in practice, a different approach can be used: it is possible to zero out the difference in the time of flight of ions with zero energy and with a boundary energy located 2 √ 1
1⁄2 in the middle of the energy spectra with structurally fixed feasible sizes ∆ = ( ) [ 0 − 1√∆
− 2√∆ + 1 − − 3√∆ + 1(1 − 1)− 4(∆ + 1)−1⁄2], where dependence on energy calculated in two ways. On the left, the characteristics obtained for exact sizes are shown, on the right, the characteristics obtained for a device with an 5% linear dimensions error, which is permissible for electrodes and grids as single piece produced parts. The peak on the graph corresponds to the selected boundary energy, at which the area under the resolution curve is maximum in the region of interest of the energy spectra. between the grids and the voltage at the electrodes, however, the dimensions along the radial coordinate and the approach to spatial focusing require volume modeling.
B. Two-dimensional axisymmetric model
The initial data obtained as a result of a one-dimensional calculation are insufficient for a complete design, two parameters are also necessary - the target diameter and the distance to the ion receiver.
Based on our previous prototyping experience, we selected a target diameter of 24 cm. The position of the ion detector, as well as the focal length of a parabolic ion
mirror, was determined by the design and ease of manufacture.
The verification of the calculation results was carried out in two stages. At the first stage, a simulation of the structure was carried out with length deviations of the field-free path from the nominal one, the simulation results are shown in
Length of the
Field-Free
Area, mm
To analyze the two-dimensional case, we used the CPU
implementation of the algorithm described in detail in [
Approximately, the initial temperature of the plasmoid was determined according to the formula: 0 = 0.1 ∙ (V0 (1 + √ρρti) −1 ), microparticle density to target density.
where 0 is the microparticle speed, ρi is the ratio of ρt
The distribution of ion velocities in a plasmoid, which is a multicomponent plasma depending on temperature, obeys the Maxwell distribution:
q( ) = √π2kmTjj exp (− 2 2), where is the total plasma charge, j is the mass of ions, is the Boltzmann constant, is the temperature, ηj is the fraction of j-type ions in the total plasma.
To generate a given probability distribution, the BoxMuller algorithm was used. To calculate the spectra, a module was written to calculate the number of ions that hit the receiver per unit time with a given sampling frequency (or the width of the time window).
The step-by-step algorithm of the program on a triangular grid does not differ sufficiently from the one described above, with the exception of the last paragraph.
1. Loading data on the computational grid with a field from a file.
2. File parsing: linking nodes, triangles, areas and field values.
3. Creating a Mesh object with a description of the relationships of nodes and triangles.
4. The formation of a model ion packet based on the given coordinates and the interaction speed.
5. Finding the current triangle for each ion. 6. Interpolation of the field at the location of each ion. 7. Calculation of the displacement of each ion over time dt.
8. Checking the location of the ion in the current triangle.
9. The recursive search for a new triangle. 10. Checking for ion loss or detection. 11. Repeat steps 6-10.
12. Upon reaching the maximum calculation time, stop and count the detected ions per unit time.
During experimental testing at the dust particle
accelerator [
The analytical calculation and two-dimensional modeling allowed to obtain a significant amount of information about the device operation and to select the optimal design parameters that can provide an increase in the collection coefficient and resolution with the same low weight-size parameters, which is almost impossible to obtain as a result of full-scale experimental testing.
The simulation results showed good convergence with the experimental results and confirmed the applicability of this approach to solve the design problems of more complex time-of-flight sensors.