ESS 265

Chapter 6. Deep Space Instrumentation

 

6.1 Plasma Analyzer Design

If you were studying the "thermal" population of a plasma you might want to know its density, flow velocity, its temperature and any anisotropics in that temperature, its organization relative to the magnetic field, whether its distribution function, f(v), differed from a maxwellian distribution, its elemental composition and charge states and its isotopic composition. If the instrument you are designing to measure some or all of these properties of the plasma is to be flown on a spacecraft you have to worry about the accommodation that the spacecraft provides for you. What you can build will be limited by the power available for the instrument and how much mass and volume are available in the payload. The stabilization of the spacecraft is also an important design consideration because detectors can only view a portion of the 4 steradians surrounding the spacecraft. Thus, multiple detector heads may be necessary. If the spacecraft is spinning, the spin helps scan the region surrounding the spacecraft but too rapid a spin limits the count rate while too slow a rate limits the temporal resolution of the data. One has to worry about the electrostatic cleanliness of the spacecraft so that the spacecraft is close to an equipotential surface and if possible remains at near zero potential. Sometimes active potential control is needed.

One must understand what plasma environment will be encountered. Will the plasma be a cold beam like the solar wind or a hot plasma such as the Earth's plasma sheet? Will there be an intense radiation belt that will both give false counts in the instrument and decrease the expected life of the instrument? What is the resolution required in time, angle, energy and mass per charge to achieve the scientific objectives? What is the range required in energy and density to measure the plasmas encountered and what telemetry rate is available to transmit all this information back to Earth?

Plasma instruments also require the use of high voltages, they generally need some control circuitry to be adjusted in flight and they need thorough calibration both prelaunch and post-launch. Finally, as all space instrumentation the instrument must be built to function reliably for a long period in space and be built under often severe cost constraints.

6.1.1 The Faraday Cup

Two types of plasma detectors are in common use in deep space plasmas: Faraday cups and electrostatic analyzers. Figure 6.1 shows the cross sections of a typical Faraday cup plasma analyzer. A grid with a voltage that steps between V1 and V2 creates a square wave of current on collectors at the rear of the cup. Ions with energy less than qV1 are reflected by the potential. More energetic ions pass through to the collector. When the grid potential is modulated with potential, V2, ions with energy less than V2 are reflected. The difference in flux as the instrument steps between, V1 and V2, gives a measure of the flux of particles hitting the spacecraft in the energy range between qV1 and qV2. By modulating between V2 and V3, one can measure in the range qV2 to qV3, etc.

The current collector at the back of the detector may be segmented in order to get angular information. This was done on Mariner 2, Imp 8, and OGO-5. On Voyager three separate cups with different normal directions were used. Figure 6.2 shows a 120 degree, 3 sector, detector as used on Mariner 5 to obtain plasma flow directions both in the ecliptic plane and out of it. The data from this instrument was able to show that Alfven waves were present in the solar wind, propagating outward from the sun [Belcher and Davis, 1971]. We note that such a detector provides only a reduced distribution function along one vector direction.

6.1.2 The Electrostatic Analyzer

An electrostatic analyzer uses an electric field between two curved plates to guide the flight path of a charged particle around a bend to a detector. The detector then can be out of view of photons from the Sun. Nevertheless, stringent measures are often required to keep sunlight from travelling down between the plates including blackening and the use of serrated edges on the plates. Three configurations of concentric plates are shown in Figure 6.3. On the left is a pair of cylindrical plates. In the middle are spherical plates and on the right is a so-called top hat design leading into a pair of spherical plates. Particles are admitted into the first two detectors over a limited path length. This length together with the size of the detector at the end of the curved plate defines a geometric window as shown. The top hat analyzer views a full 360 degrees in azimuth with a narrow fan in the orthogonal direction.

The force balance on a charged particle moving through the curved plate analyzer is shown in Figure 6.4. The electric field exerts a force qE on the particle that causes it to move in a great circle with radius r equal to mv2/qE. If the two plates have radii R1 and R2, the analyzer constant k is equal to 0.5 (R1 + R2)/(R2-R1). The bending angle is phi. It can range up to 180o in most detectors. The greatest focusing is achieved at this bending angle. The flux of plasma that enters the instrument is determined by the size of the aperture, A. The size of the detector, the voltage range and the polarity affects the energy and species detected. The viewing geometry is also dependent on the placement on the spacecraft. On ISEE 1 for example two electrostatic analyzers with fan beams at an angle to each other we used on a spinning spacecraft to determine the flow direction in both the ecliptic plane and out of it. Figure 6.5 shows the cross-section of the IMP 7 and 8 plasma analyzer that simultaneously measured electrons and ions.

The spherical slit of a curved plate analyzer allows particles to pass through the analyzer over a range of entering angles and energies as illustrated for one incoming particle in Figure 6.6. The equation shown in this figure allows the radius of the particles orbit to be drawn as a function of azimuthal angle along its flight path. If that radius exceeds the outer radius of the slit the particle will be absorbed and not reach the counter at the end of the slit.

Figure 6.7 examines for various incident angles the range of velocities allowed through the slit to the detector for four bending angles 70 deg; 90 deg (a quadisphere), 130 deg; and 180 deg (a hemisphere). This plot demonstrates that the hemispherical analyzer has the narrowest energy range and most constant as the incident angle varies. One can calculate the response as a function of the incidence angle integrated over the velocity, the distance of the particle from the center of curvature of the analyzer and the angular location of the entrance of the particle along the face of the slit. This is shown in Figure 6.8 together with actual calibration curves for an analyzer with a 90 deg. bend. Particles that arrive nearly normal to the face of the slit have a narrow, high efficiency, acceptance window. The efficiency falls to a maximum of 60% at an incidence angle of 25 deg. and broadens from 7o full width half maximum (FWHM) to 10o. When the angle of incidence reaches 50 deg. the maximum efficiency has dropped to 30% and the FWHM has increased to 20 deg. Fringing fields cause the offset of the theoretical and actual curves.

6.1.3 Top Hat Analyzer

The limited field of view of the electrostatic analyzer can be overcome with design shown in Figure 6.9 called a top hat analyzer. This design has hemispherical plates but the particles enter at the top of the plates and are bent less than 90 degrees. The top plate above the entrance to the analyzer helps guide the particles into the slit. A sample trajectory is shown by the dashed line. The resulting field of view is a narrow fan that extends completely around the detector. A segmented collector at the bottom of the detector provides angular resolution. If the spacecraft spins about an axis that lies in the plane of the fan beam then the fan will sweep out all of solid angle space each rotation. If the spacecraft is three-axis stabilized then another means must be adopted to provide that sweeping. A partial solution is the use of deflection plates along the entrance path as shown in Figure 6.10. If two top hat analyzers are mounted on a three-axis stabilized spacecraft with their fans orthogonal, deflector plates can enable the detector to scan above 70% of the solid angle around the spacecraft.

6.1.4 Moments of the Distribution Function

The detector on the back end of an analyzer returns counts. In order to convert the count to physically useful quantities we must apply calibration factors. The basic quantity we wish to compute is the distribution function that gives the number of particles at the detector per unit volume in configuration space and per unit volume in velocity space. This can then be used to calculate moments such as the density, temperature and velocity. The number of counts, c, measured by a detector in time , is:

where v is the particle speed, v is the velocity f(v) is the distribution function d3v is the velocity space element sampled by the analyzer in time , A is the entrance aperture area, and is the detector efficiency. The integral is over the instantaneous acceptance of the analyzer.

We can rewrite d3v as:

For a given analyzer the product <(dvd)/v> is a constant, W. If the resolution of the analyzer in energy and angle is good compared to the scale size for changes in the distribution function, then W can be removed from inside the integral in equation (1).

We define the geometric factor of the detector as AW so that the counts as a function of speed and angle can be written:

If the plasma is hot then the distribution function varies little over the - acceptance of the analyzer and

We can now calculate the moments of the distribution function

If the plasma consists of a cold beam in which the thermal velocity was less than the bulk velocity, the count rate as a function of the energy per charge and azimuth (on a spinning spacecraft) might look like shown in Figure 6.11. The moments can be calculated in an analogous way here but we see that unless we arbitrarily truncate the integration at some energy per charge the moments will be in error because of the presence of ions heavier than protons. In the case which is typical of the solar wind beyond 1 AU the alpha and the proton peaks are well separated. Inside 1AU as the distance to the sun decreases the temperature rises while the bulk velocity remains the same and the alpha and proton peaks exhibit greater overlap. This same hot condition can be found behind collisionless shocks whether they be planetary or interplanetary in origin. In order to obtain accurate moments under these circumstances we need to have a means to measure the composition of the plasma, or more correctly measure the distribution function of each species separately.

6.1.5 Plasma Composition Measurements

The plasma composition is often quite variable and is an important diagnostic for the origin of that plasma. Figure 6.12 shows an example of the plasma moments seen during the passage of an interplanetary coronal mass ejection (ICME). The bottom trace shows the relative abundance of alpha particles. A period of enhanced alpha density is entered shortly after the drop in proton temperature that signals the entry into the ICME proper. The counts as a function of energy per charge are shown for this interval in Figure 6.13. Once the shock is crossed it is very difficult to distinguish the alpha and the protons. It is not until the relatively cold interior of the ICME is encountered that the alpha particles are readily separated from the protons. The interval even includes a period in which singly ionized helium is present.

Another example of the importance of measuring composition is shown in Figure 6.14. The upper left panel illustrates the context of the measurement. The spacecraft is close to the magnetopause reconnection is occurring and plasma from both the magnetosheath and the magnetosphere is being encountered. The panels on the upper right and lower left show angular scans of the distribution function near the magnetopause. In these plots all ions are included and assumed to be protons. However, we have evidence that there are multiple ions present. This evidence is shown in the lower right panel that shows an energy per charge spectrum with peaks at not only the proton energy per charge but also singly ionized helium and oxygen peaks. Clearly the source of this plasma was the ionosphere and not the solar wind. The solar wind contains insignificant amounts of singly ionized oxygen, and singly ionized helium is very rare.

There are three detectors that can be used to provide mass composition: electrostatic analyzers, magnetic mass spectrometers and time of flight instruments. As we have seen, the electrostatic analyzers can successfully perform this separation only when the thermal velocity of the ions is much less than the bulk velocity. The magnetic spectrometers provide good spectral resolution but are complex, slow, massive and have stray magnetic fields that may affect other measurements. Moreover, they have a limited field of view. Time of flight instruments are now available that have good sensitivity, can view all species simultaneously and have a broad field of view. The disadvantage of these instruments is that generally they have modest M/Q resolution. They also can generate an enormous amount of data.

A simple time of flight analyzer is sketched in Figure 6.15. When the ion leaves the analyzer section it passes through a very thin carbon film. This passage knocks out an electron that is captured by a positively charged plate and triggers a start pulse. When the ion reaches a stop plate another pulse is generated and the time between the pulses is the time of flight. The energy loss and angular spreading caused by the passage through the foil degrades the M/Q resolution here.

An improved analyzer can be made using a section containing a linearly increasing electric field in the post analyzer region. This is shown in Figure 6.16. The front and analyzer is a top hat. As the ion exits the electrostatic analyzer it is accelerated through the carbon foil into the linear electric field. The electron produces a start pulse and the ion when it gets reflected back to the top of the linear electric field chamber stops the timer.

The equation of motion of the ions in the linear electric field section can be calculated as follows. The electric field as a function of distance along the axis is:

Ez = -kZ

The force on the ion is:

Solving for z we obtain

Thus the time of flight is (m/kq) and is independent of the initial speed and direction of motion. Figure 6.17 shows an example of the output of such device. It clearly has excellent mass resolution.

 

References

Belcher, J. W. and L. Davis, Jr., Large amplitude Alfven waves in the interplanetary medium II, J. Geophys. Res., 76, 3534-3563, 1971.  


6.2 Plasma Wave Instrumentation

Groundbased measurements of naturally occurring electromagnetic signals have been made for over 100 years. Some of these such as the descending tone known as a whistler are due to lightning generation in the atmosphere. Others are due to processes in the distant magnetosphere. The first satellites to study very low frequency (VLF) frequencies were the Alouette 1 spacecraft launched in Sept. 1962 and the Injun 3 spacecraft launched in Dec. 1962. Alouette 1 carried an electric dipole antenna and Injun 3 a magnetic loop antenna. We first examine the electric dipole antenna.

6.2.1 Electric Field Antennas

Two types of electric dipole antenna are in common use. These are shown in Figure 6.18; the cylindrical probe that is essentially two wires extending into the plasma from either side of the spacecraft; and the spherical double probe that consists of two spherical balls that make contact with the plasma but have externally non-conducting lines that connect the spheres to the spacecraft. The radius of the spheres is generally about 10 cm and the length of both types of antennas ranges upwards of 100m tip to tip. The spheres usually contain a preamp and can be actively controlled.

The effecive length of an antenna is the voltage seen by the antenna divided by the applied electric field if the wavelength of the wave is much larger than the length of the antenna that is usually the case. It is usually estimated from geometry but has occasionally been calculated from simultaneous measurements of the oscillating magnetic field. Dipole antennas are used because the monopole is susceptible to interference from the spacecraft and its effective length is less well known.

Figure 6.19 shows the geometry of the sheath of plasma that forms around a cylindrical electric dipole antenna. The electric potentials in the plasma couple to the antenna via the sheath resistance Rs and the capacity Cs. If the Debye length is small compared to the antenna length and the frequency of the waves is much less than the plasma frequency then the effective length of the antenna is close to half the tip to tip distance. Two regimes can then be treated. The antenna is resistive when the frequency, , is less than (RC)-1 and capacitive when it is above (RC)-1. The equivalent circuit of the antenna and its preamplifier is shown in the bottom of Figure 6.19. If the instrument is to act like a voltmeter then the resistance of the preamplifier, RL, should be much less than that of the sheath Rs when resistively coupled and the capacity RL much greater than Cs when capacitively coupled. The situations in which the density is low and the frequencies are high are much more difficult to analyze.

For a spherical probe of radius R the antenna capacitance in a vacuum is 4 oR and for a cylindrical antenna of length, L/2, and diameter, a, it is oL[ln(L/a)-1]-1. Typically a spherical probe will have a vacuum capacitance of 10 pf and a cylindrical antenna 300 pf. The capacitance in a plasma with a finite Debye length, D, will be altered. For a spherical probe the capacitance is 4 oR[1+R/D]. For a cylindrical probe of "effective length" L/2 the capacitance is oL [ln(D/a)].

There are two sources of noise in the plasma wave receiver: plasma shot noise and preamp current noise. Usually FET preamplifiers are used to provide the lowest noise. In order to reduce the shot noise due to impacts to as low a level as possible we wish to make the diameter of the wire or sphere as small as possible. This desire is in direct competition with the need noted above to keep the capacitance as high as possible.

Finally, we note that electrostatic waves can have short wavelengths, comparable to or less than the length of the antenna. In this situation there can be nulls as the negative and positive potentials cancel along the length of the antenna. If the spacecraft is rotating as shown in the bottom of Figure 6.20, the nulls will vary with time and frequency in a characteristic pattern. The top panel of Figure 6.20 shows the expected power spectrum for different wavelengths for a spherical double probe and a cylindrical probe at fixed orientation.

6.2.2 Magnetic Antennas

Two types of magnetic antennas are in common use: loop antennas and search coils . Schematic diagrams of these two antenna are shown in Figures 6.21 and 6.22. Both antennas work on the principle that according to Faraday's law whenever the magnetic flux enclosed by a conductor changes a voltage is induced in that conductor. If the area of a coil is A and it has N turns then the voltage induced is Ndm/dt where m is the magnetic flux i.e. the scalar product between the magnetic field vector and the vector area whose direction is along the normal to its surface. The search coil uses a permeable core of length much greater than the coil of wire in which the voltage is induced to concentrate the magnetic flux through the coils.

The noise level is generally determined by the resistance in the wire and a key design consideration is to minimize mass in space applications. The resistance of a loop is 2RN/a2 where R is the radius of the loop, a is the radius of the wire, is the electrical conductivity of the wire and N is the number of turns. The mass of this loop, m, which is to be minimized is 22a2 Rn where is the density of the wire. One can show that the noise power spectral density in T2/Hz is 2kt/(mf) where t is the temperature of the wire, k is Boltzmann's constant and f is the wave frequency in Hz. This expression is independent of both the size of the coil and its number of turns. Thus the noise of the magnetic antenna depends on choosing a material with the smallest possible ratio of density to electrical conductivity when the mass of the antenna is fixed. Aluminum is the best such material, although copper and silver are close. It is easy to prove that the optimum shape of the coil is circular as we have assumed in the above discussion. It is also obvious that an antenna will produce a larger voltage, one that needs less electronic amplification, the larger it is.

The search coil creates an effectively larger antenna by using a highly permeable core to concentrate the magnetic flux in the coil. Similar design considerations regarding noise apply here but the mass of the core and its length relative to the winding complicate determining the optimum configuration. Typically a search coil has half its mass in the core and half in the windings.

The practical bandwidth of a search coil is limited by its inductance and capacitance that produce a resonance frequency = (LC)-. The equivalent circuit shown in Figure 6.23 attempts to damp the resonant response of the magnetic antenna and broaden frequency range. The minimum inductance is achieved with a single loop of wire. This produces the greatest bandwidth but then the resistance noise of the antenna becomes too low and it must be coupled to the preamplifier with a transformer that produces a low frequency cut off of about 50 Hz. Thus, the push to higher frequencies has an affect on the lower frequencies and the bandwidth of the loop antenna has a finite limit.

The search coil uses a large number of turns and avoids the coupling transformer but also reduces the cross section of the wire to maintain fixed mass. The noise level of the preamplifier that must be exceeded by the resistance noise of the wire then sets the inductance of the search coil and affects its bandwidth. To complete our look at the optimization of the design of magnetic antennas we note that the capacitance of the loop antenna is set by the secondary winding of the transformer and the capacitance of the search coil determined mainly by the capacitance of the coil itself. With a search coil flux feedback is sometimes used to modify the high frequency response. Figure 6.24 compares the frequency response of a typical loop antenna with that of a search coil.

6.2.3 How Many Antennas to Carry

Since there are three vector components each of the electric and of the magnetic oscillations associated with plasma waves, a plasma wave investigation has the potential for becoming quite massive. Moreover on a spinning spacecraft the deployment of long antennas in the spin place is much easier than along the spin axis. Thus it is critical to examine the science return enabled by instrumentation of increasing complexity.

A single electric antenna allows for the survey of the radio and plasma wave environment such as on a first discovery mission, like Voyager. It is most efficient at radio wave frequencies. It can detect electrostatic waves that have no magnetic signature. The power spectral density in selected frequency ranges, such as on the Pioneer Venus wave instrument, can be sampled but waveforms allow more resolution and diagnostic information. Carrying both a magnetic and an electric antenna increases the mass somewhat but enables electrostatic and electromagnetic modes to be distinguished. While joint operation of the two antennas is preferred, useful information can be obtained by toggling between the antennas. This minimizes the added circuitry for the second antenna.

One electric and three magnetic antennas enable wave normal analysis of electromagnetic waves and the determination of the sign of the Poynting flux that tells the direction of energy flow. The electronics complexity increases because simultaneous sampling and the presentation of phase information is required. The data rate requirements or onboard computation requirements increase substantially for this option. Occasionally, such as in radio astronomy two electric field components are used to do direction finding under simplifying assumptions. This requires a second receiver for the electric antennas and a cross-correlator. The data rate is also increased.

Two electric and three magnetic antennas enable wave-normal analysis and Poynting vector determination under simplifying assumptions. Radio frequency direction finding can be done as above. Here a five-channel receiver is needed as well as a commensurate increase in the data rate. If all three magnetic and three electric components are measured then the wave normal analysis and Poynting flux determination can be done with no assumptions. Two dimensional radio direction-finding can be done and the full Stokes parameter determination can be achieved. Needless to say this requires the greatest complexity of instrumentation and the highest data rate.

6.2.4 Data Return

Although the bandwidth of data systems on modern spacecraft is often quite large, the data rate required to cover the complete plasma wave and radio spectrum in both magnetic and electric components could quickly swamp the best of them. For example if one were to sample at a rate of 10 MHz, all six components at a resolution of 12 bits one would need a 100 MHz data rate for this one instrument above. Various strategies exist for lowering this rate. Editing, so that only occasional bursts of data are recorded and later transmitted, is one strategy but risks missing events and phenomena. In order to have some information at all times, multichannel analyzers such as the one whose functional block diagram is shown in Figure 6.25 are used. The signal is split and sent through a bank of filters and the power of the signal at each frequency is recorded. A sample output from such a device is shown in Figure 6.26. If the filters are spaced closely enough so that there are no deep gaps between them, few signals will be missed. However, the rise time and averaging time of the detectors can attenuate brief signals.

A second approach to signal detection to avoid frequency gaps is the sweep frequency detector shown in Figure 6.27. This detector converts the wave frequency to a higher frequency by mixing it with a variable frequency and passing it through a narrowband filter. This is quite useful for quasi-time stationary signals but is not useful for rapidly time varying signals as those produced by lightning discharges. An example of output from sweep frequency analyzers is shown in Figure 6.28 from a perijove pass of the Galileo spacecraft. Figure 6.29 shows 22 minutes of data in a range of frequencies from 63 to 88 kHz obtained in the Earth's magnetosphere in the region of the plasmapause. Much structure can be seen in these spectra but little can be done to analyze the wave properties.

If one wants full flexibility to analyze the properties of waves when the data are returned from the spacecraft, one must transmit a high fidelity version of the waveform. In the early days of the space program this was done by frequency modulating a carrier signal but now it is done digitally. Figure 6.30 shows a functional block diagram of a wideband receiver. Advantages of digital recording include improved dynamic range, greater precision, storage for later and perhaps lower rate playback and signal compression. Figure 6.31 shows some unducted magnetospheric whistlers seen by the Polar plasma wave instrument using the magnetic antenna connected to the wideband receiver. Figure 6.32 shows 50 seconds of data of auroral kilometric radiation captured with the Polar electric antenna using the wideband receiver. In stark contrast to the 50 seconds of spectra above, Figure 6.33 shows 16 years of Voyager spectra in the interplanetary medium showing bursts of noise believed associated with the heliopause. The most intense bursts occur once a solar cycle and last many months, but smaller bursts are seen between the two large events that are also probably associated with the heliopause. In this plot waveforms are sampled only occasionally with long data gaps in between but plotted in such a way that the data gaps are not shown. This technique of data compression works well for signals that change very slowly with time such as those shown here.

The availability of waveforms allows detailed analysis not possible with coarse samples of the power as provided by the spectrum analyzer channels. Figure 6.34 shows power spectral density plots of the thermal noise of the solar wind electrons at 1 AU on ISEE-3. The shape of the spectrum has been accurately modeled to yield the number density and temperature of the core and halo components of the solar wind.

In summary three different approaches are used to return the information obtained by plasma wave receivers in deep space. Each has important advantages as detailed in Figure 6.35. When data rates are low the multichannel analyzer provides good temporal resolution for minimum telemetry rate. The sweep frequency analyzer gives good spectral resolution at a higher data rate. Waveform sampling, however, is the ultimate tool for analysis but is expensive of bits. Data compression techniques have been tried and may see even greater utilization in the future. One innovative use of data compression has been on the Galileo mission where spectra were calculated on board and then image processing data compression techniques applied to the dynamic spectrum to bring the data back. This procedure enabled measurements to be returned that would have been impossible otherwise.

6.25 Two examples of Plasma Wave Instruments

In the sections above we have provided examples of plasma wave measurements of different phenomena. Here we show two examples of how the parameters of two plasma analyzers were selected to study the plasma waves in the magnetospheres of Jupiter and Saturn. Figure 6.36 shows the frequency channels selected for the spectrum analyzer on Voyager and the bandwidth of the waveform channel compared with the characteristic frequencies to be expected for waves in the jovian and saturnian magnetospheres. Figure 6.37 shows the bands of the various receivers compared with a schematic spectrogram of the expected phenomena to be seen in the saturnian magnetosphere. Figure 6.38 shows the functional block diagram of the Cassini plasma wave analyzer. Figure 6.39 shows the placement of the antennas on the spacecraft. The three electric field antennas provide two nearly orthogonal measurements of the electric  


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