A compact electrostatic dust accelerator mainly consists of one high voltage power supply, one dust source, one focusing lens, dust detectors, target chambers and a high vacuum system. Our previous small accelerator is shown in
Figure 1. A schematic diagram of our upgraded small dust accelerator with the PSU with 3 additional dust detectors and deflection stage is given in
Figure 2. The test setup of the linac stage consists of one dust source, one focussing system, one differential dust detector (2 CSA channels), the linac stage and one single end dust detector after the linac (see
Figure 3).
The dust source is the heart of an electrostatic dust accelerator first developed by reference [
4]. The dust source in small accelerators serves two purposes: charging dust particles and accelerating them to final speeds. Dust particles are filled into the reservoir during assembly. A pulser unit connected to the reservoir applies a time-varying electric field between the needle and the reservoir. Dust particles are charged, lifted and pushed through a small hole out of the reservoir. A grounded extraction plate further accelerates charged particles to their final speeds. A beam collimator system with grounded metal rings with a diameter of 0.8 mm leads particles into the accelerator beam line. The entire accelerator employs a high-vacuum system to avoid sparking caused by the high electric field strength in the dust source.
Dust particles are fired from the dust source using a potential difference of the needle to ground. After exiting the collimating system, the dust particles are focused with an electrostatic lens. The accelerated dust particles are characterized while passing the dust detectors. The upgraded beam line provides two test locations: (1) Test chamber 1 is close to the dust source and is suitable for high-frequency particle experiments, especially for particles with speeds around tens m/s; (2) Test chamber 2 can be used together with the PSU (and/or linac) for experiments with particles in specific selection windows with higher speeds.
The velocity obtained by a particle in an electrostatic field depends on its charge-to-mass ratio and acceleration voltage. If a particle of mass
m and surface charge
q is accelerated through potential
, the speed
v is obtained from the energy law by:
2.1. Dust Source Upgrade
The charging of dust particles is crucial for electrostatic acceleration. Particles may be charged with UV irradiation [
16], electron and ion beams, or contact with a charged surface. The latter method, which results in an adequate particle charge-to-mass ratio (
), was utilized to develop the dust source in the electrostatic accelerator. The newly upgraded dust source is based on our previous design described in [
17], which mainly consists of one vacuum housing, one dust reservoir, one needle electrode and one collimating system (see
Figure 4). The dust reservoir has a cylindrical shape with a length of 25 mm and a diameter of 12 mm. The 1 mm tungsten needle is very sharp and has a tip diameter in the range of 1–4 μm, which is centered in the cylinder axis of the dust reservoir and aligned to the accelerator beam line. The dust reservoir itself lies on the same electric potential as the needle and is pulsed down frequently to blow up the dust powder. Conductive dust particles are filled into the reservoir. The electric field will induce a charge on the surfaces of single particles and lift them up. Whenever these levitated particles hit the needle tip, they obtain higher electric charges and are ejected. The accelerated dust particles have to pass through a small hole (0.8 mm in diameter) in the extraction plate and after a collimation system they enter the beam line.
Conductive dust particles can obtain surface charges by contact with highly charged surfaces [
16]. The surface charge of a spherical particle with radius
r under vacuum permittivity
and surface potential
is given by:
All particles obtain their final speeds from the dust source in a dust accelerator, shown in
Figure 1. For a dust particle of a given radius and density, its final speed is only dependent on the high voltage added in the dust source. As a result, the high-voltage interface used in the dust source has been modified and redesigned. Our new design allows input voltages up to 40 kV through two ceramic feedthroughs (CeramTec) (see the right side of
Figure 4). Furthermore, the mechanical designs of the dust reservoir and isolator are simplified to reduce the number of assembled parts and optimise the evacuation by the vacuum pump. The simpler and lighter structure of the new dust source allows an easier handling and a faster dust refilling. The parameters of our upgraded dust source are summarized in
Table 2.
2.2. Focusing System Upgrade
In order to collimate dust particles, a focusing system located behind the dust source is needed. Charged dust particles can be focused using electric fields (electrostatic force) or magnetic fields (Lorentz force). We compared two electrostatic lens systems (a single-cylinder system and an einzel lens system, see
Figure 5) in the small accelerator with an acceleration voltage of 15 kV. The shape of the single-cylinder focusing system is similar to the one used in our 2 MV dust accelerator facility [
6]. The particularly shaped metal cylinder with an inner diameter of 8 mm is directly behind the dust source. The einzel lens consists of three separated cylindrical electrodes. The central electrode is connected to high voltages to generate lens effects and the other two electrodes are grounded.
The relation between the focal length and electrode potential is shown in
Table 3. The focal length is calculated between the dust source and the focal point. The focal length is affected by the electrode geometry and focusing and acceleration voltages. Based on our simulation results and operation experiences, for a given acceleration voltage, the focal point of the dust beam is altered by varying the potential of the focusing electrode according to the experimental requirements.
2.3. Dust Detector Upgrade
The dust detector is needed to monitor the particles launched by the dust source. It is based on charge induction and enables the non-contact measurement of individual dust particles down to the sub-micron range. Positively charged dust particles attract electrons and induce electron movement in metal electrodes. A charge sensitive amplifier (CSA) connected to the electrode transforms the induced charge to an equivalent voltage, which is evaluated using the detection system. In order to measure hypervelocity dust particles with surface charges down to 0.1 fC, Srama [
18] developed a low-noise dust detector. The dust detector employed a copper cylinder electrode with a diameter of 9 mm and a length (
L) of 200 mm. The particle velocity (
v) is determined by the flight time (
T) through the electrode (Equation (
3)).
Such a dust detector has a very high accuracy in the measurement of low- and high-speed particles up to
. However, the integrated Amptek A250F/NF CSA in the design has a lower cutoff frequency of 2 kHz, which restricts its application in the measurement of dust particles with speeds below 100 m/s launched by small accelerators. In contrast, our upgraded dust detector consists of four short cylindrical tubes each 5 cm in length and 0.9 cm in inner diameter (see
Figure 6). The electrodes are surrounded by two cylindrical Faraday caps to restrain any interference of environmental charges or electromagnetic fields. The electrodes are shielded from each other by grounded grids and insulated by Polytetrafluorethylen (PTFE) supports. The connection of two sensor electrodes to one single differential CSA further reduced the influence of common mode interference. The screening by the shielding cylinders is improved by attaching larger meshes. The electrodes and CSAs are mounted in a 100 mm vacuum pipe with standard CF 100 flange interfaces.
The design of the differential CSA is based on an improved version of the design presented in reference [
19]. While traditional CSAs evaluate the influenced charge of a single electrode with reference to ground, the detector presented in this paper contains two electrodes and evaluates the charge difference between both electrodes. This results in a bipolar output pulse as given in
Figure 7, which in subsequent designs will be filtered with a matched-filter system. The amplifier Application Specific Integrated Circuit (ASIC) is designed in a
technology. It has a 3 dB frequency range from
to
and therefore is able to accurately reproduce the influenced charges even of very low-speed particles. The low cutoff frequency of
is achieved by replacing the feedback resistor
typically required for CSAs with a MOSFET in an off-state. This enables the design to reach an effective feedback resistance in the tera-ohm range. To stop the amplifier from leaving the correct operating point due to leakage currents, a reset pulse is applied to the amplifier every few seconds. During this pulse the MOSFET in the feedback path is transferred to the linear region. Thereby, the feedback resistance is lowered significantly and the correct input voltage is reestablished.
Additionally, materials with a very high specific electrical resistance are used for all parts with contact to the input of the amplifier. The input stage of the amplifier consists of MOSFETs with a differential input capacitance of
. The feedback capacitors have a value of
. In the laboratory test the amplifier offers a very low equivalent noise charge of
(0.028 fC) in the frequency range from
to
for a differential detector capacitance of
, which is already heavily affected by dielectric loss noise of the PCB and the detector capacitance. In the accelerator setup the amplifier noise is dominated by interferences that mechanically couple into the detector electrodes, as visible in
Figure 7.
The potential of the electrode is unbalanced by a negative charge of the same amount as the positive charge on the accelerated dust particle. The difference to the voltage amplification of a charge sensitive amplification is the capacitance
in addition to a resistor
. A better sensitivity could be achieved with a matched-filter-based evaluation that considers both the positive and negative part of the signal. For the simple case of a positive-only evaluation, the particle will induce a charge in one of the electrodes, resulting in a charge gain for an ideal amplifier of:
For the measurements, only one output of the differential CSA is recorded; assuming a sufficient common mode suppression, the output voltage is therefore divided by two, resulting in:
Before digitizing, the signal is passed trough a simple bandpass filter and further amplified by a factor of 2.5, resulting in an overall charge gain of .
2.5. Post-Stage Linac
According to Equations (
1) and (
2), the final particle speed launched from the dust source depends on the particle size, the material and the potential of the needle electrode. The dust speed can be increased by increasing the voltage connected to the dust source. Unfortunately, intense high voltages at the needle can cause field emission and they can destroy the sharp tip [
4,
20]. A later acceleration stage is necessary to obtain more high-speed particles. Therefore, we developed a compact linac (see
Figure 9) with a 600 mm long vacuum pipe with standard CF 100 flange interfaces. The linac has 6 drift tubes with an inner diameter of 40 mm.
When a particle passes the differential detectors, two signals are generated by the differential detector and sampled with a field-programmable gate array (FPGA) to calculate the particle speed. Taking the accelerating voltages of the dust source and the linac into account, the FPGA calculates the pulse train necessary to switch the polarity of the drift tubes as a particle passes through in real time. A high-voltage circuit constantly charges the drift tubes to −20 kV. When a positively charged particle approaches a drift tube, it is attracted and therefore accelerated. When it reaches the center of the drift tube—which acts like a Faraday shield—and the FPGA signal arrives, the tube is grounded by a high-voltage MOSFET switch. In this way, the particle sees an accelerating field again as it leaves the tube. An initial setup, with a 16 kV dust source voltage and 16 kV in 5 linear acceleration stages, increased the final speeds of particles by a factor of about 2.23 (see
Figure 10). Due to electromagnetic compatibility (EMC) problems, the high voltage supply is currently being rebuilt.