Evaluation of waveform data processing in Wave-Particle Interaction Analyzer
© Hikishima et al.; licensee Springer. 2014
Received: 7 January 2014
Accepted: 17 June 2014
Published: 1 July 2014
The Wave-Particle Interaction Analyzer (WPIA) is a software function installed on the Exploration of energization and Radiation in Geospace (ERG) satellite. The WPIA directly measures the quantity of energy transfer between whistler-mode chorus waves and resonant energetic electrons by using plasma wave vectors and velocity vectors of plasma particles. The phase differences of the WPIA require accurate phase angles of waves and electrons in order to statistically evaluate the significance of the quantity of energy transfer. We propose a technical method for efficient waveform processing in order to conduct the WPIA measurement precisely. In the WPIA measurement, the various waves detected by the onboard instrument appear as noise in the calculation of the quantity of energy transfer for whistler-mode chorus waves. The characteristic frequency variation of the chorus waves makes waveform processing difficult. A chorus waveform is used for the WPIA processing through passband filtering by selecting appropriate data processing length and frequency resolution. We implement overlapping processing of wave data in order to reduce the induced error of the wave phase. The results of waveform processing indicate that the phase errors are successfully reduced and statistical fluctuations are suppressed. The proposed waveform processing method is a necessary and applicative processing for the calculations of the WPIA in the ERG mission.
The Wave-Particle Interaction Analyzer (WPIA) is an instrument package installed in the Exploration of energization and Radiation in Geospace (ERG) satellite (Miyoshi et al. 2013). The WPIA, which directly measures the energy transfer in the process of wave-particle resonant interactions between plasma waves and charged particles in the space plasma environment, is equipped as a software function. Whistler-mode chorus waves are commonly observed outside the plasmasphere, and the waves can cause resonant interactions with energetic electrons in the kinetic energy range from a few keV to a few MeV. The whistler-mode chorus waves are also considered to be a candidate for inducing relativistic electrons of MeV energy during a magnetic storm in the inner magnetosphere (e.g., Summers et al. 1998; Meredith et al. 2002). In the ERG mission, the primary goal is to clarify the acceleration process of plasma particles by wave-particle interactions in the inner magnetosphere. The WPIA is the first attempt to directly measure the existence of energy transfer between whistler-mode chorus waves and resonant energetic electrons in space.
The WPIA uses an instantaneous wave field vector and the velocity vector of each electron, which are measured using wave and particle instruments with microsecond resolution onboard the ERG satellite. The energy transfer W, which is represented by the inner product of E and v, where E and v are the wave electric field vector and the velocity vector of an electron, respectively (Fukuhara et al. 2009). The resonant interactions between whistler-mode chorus waves and electrons are investigated in the WPIA measurement. Whistler-mode chorus waves are generated around the equator outside the plasmapause during geomagnetic disturbances (Tsurutani and Smith 1974). Whistler-mode chorus waves appear in the frequency range below the electron gyrofrequency fce and have distinct upper and lower frequency bands, which are identified by a gap of 0.5 fce (Burtis and Helliwell 1969; Tsurutani and Smith 1974). Magnetosonic waves (MSW) and electron cyclotron harmonic (ECH) waves are often observed with the chorus waves in a region close to the magnetic equator. The MSW are equatorial electromagnetic waves that have frequencies below the lower-hybrid frequency fLHR (e.g., a few hundred hertz at L ∼ 4) (Santolík et al. 2002). The intensity approximately 200 μ V/m is comparable to the chorus wave amplitude (Gurnett 1976). The intense ECH waves are electrostatic waves and also appear with the excitation of chorus waves near the magnetic equator. The frequencies have harmonic components in (n + 1/2) fce (n = 1, 2,…) Kennel et al. (1970) with a magnitude of a few mV/m (Meredith et al. 2009). The WPIA measures resonant interactions between whistler-mode chorus waves and resonant electrons near the equatorial region. The ECH and MSW are also detected with chorus waves in the region. Such intense waves affect the wave phase of chorus waves because they appear as a superposition of waves.
In the present paper, we propose a waveform processing technique, which is required in the WPIA to accurately measure the energy transfer generated by resonant wave-particle interactions. We evaluate the effectiveness of data processing using a representative model of the chorus observed near the equator. We then present an appropriate data processing method using passband filtering and an overlapping method in the WPIA. The effectiveness of the applied waveform processing is evaluated through pseudo-WPIA measurements by the electromagnetic particle simulation.
The WPIA method
where N is the total number of particles and v i is the velocity of the i-th particle detected at time t i .
Results and discussion
Waveform processing for calculation in the WPIA
Wave data used in the WPIA processing
The specifications of the wave and particle instruments onboard the ERG satellite are described in Miyoshiet al. (2013). We introduce the measured wave data with respect to the waveform processing. Electric and magnetic sensors are installed on the ERG satellite in order to observe alternating plasma waves in space. Two wire probe antennas, which receive electric field components of plasma waves are attached in an orthogonal manner to the spin axis of the satellite. The wire antennas are sensitive to a wave vector of the electric field, where one electric field component along the spin axis is missing. For detection of the magnetic field components of waves, a three-axis search coil magnetometer, which is located on top of the mast, can detect magnetic components of the plasma wave field.
The WPIA calculation uses waveforms in the frequency range of up to 20 kHz for both the electric and magnetic wave fields. The upper frequency limit is determined by the sampling frequency of 65 kHz. Moreover, an electric waveform of up to 120 kHz with a higher sampling frequency is prepared as a special mode in order to obtain the amplitude and phase of the waveform with better time resolution. The WPIA calculation uses data of the chorus waves. However, in the frequency range of up to 20 kHz, the MSW in hundreds of hertz and the ECH waves in the kilohertz frequency band are expected to be included in the waveforms observed by the ERG satellite, which passes outside the plasmapause. Such waves are observed by the sensors as superposed waves. Intense waves result in uncertainty fluctuation in the calculation of the WPIA. Therefore, the unnecessary wave components must be removed from the received waveforms through an appropriate processing.
Evaluation of phase error in waveform processing
Parameters of the model chorus wave
Electron gyrofrequency at the equator: fce
10 kHz (L ∼ 4)
Chorus frequency (including upper
1 to 9 kHz (0.1 to 0.9 fce)
and lower bands)
Frequency sweep rate: df/dt
Duration time of a chorus element
In conducting the FFT processing, we must consider the appropriate data length of one frame used in the FFT. Since the calculation in the WPIA requires only the chorus waveform, we remove the wave mode components of the MSW and ECH waves. In order to remove the waves, we implement the passband filter applying a rectangular window with a passband of 0.1 < f < 1.0fce. The MSW waves are observed in a frequency range of a few hundred kilohertz at L ∼ 4 (Santolík et al. 2002), and the ECH waves appear in the frequency range of f > fce (Kennel et al. 1970). In order to distinguish these waves from chorus waves in the frequency domain, a frequency resolution of better than 0.1 fce is required. Considering the spectral spreading of the waves, we assume a frequency resolution of a few hundred hertz. In order to satisfy the above conditions, we assume a frequency resolution of 127 Hz, corresponding to 512 data points and a time duration of 7.8 ms in an FFT frame. A longer FFT length provides a more accurate frequency resolution and limits the increase in computation time due to repeated FFT processing, but results in an increased memory requirement.
Using 512 data points (7.8 ms) in one FFT frame
Multiplying the frame by the four-term Blackman-Harris window
Conversion to the frequency domain by FFT
Calibration using transfer functions
Using a passband filter (f = 0.1∼ 1.0f ce) to obtain the frequency band of the chorus wave
Conversion to the time domain by IFFT
Using the waveform after removing one-quarter length from both edges of the frame
Pseudo-measurement of WPIA in simulation
Number of grids
Total number of energetic electrons
Total number of cold electrons
Density ratio of energetic electrons to cold electrons
Thermal velocities of energetic electrons
at the equator, Vth∥, Vth⊥
We then conduct the pseudo-WPIA measurement using the rising chorus element obtained in the simulation. The passband filtering and overlapping method are applied in the WPIA measurement. In order to conduct the WPIA measurement, we calculate the quantity of the energy transfer W using the instantaneous waveform at a fixed point, , and the velocity vectors of resonant electrons passing through the point. We focus on the component of W that is perpendicular to the ambient magnetic field. The W component is given by the formula W=e Ew · v⊥ for the transverse component, where e is the electron charge, and Ew and v⊥ are perpendicular components of the wave electric field and the velocity vector of the electron, respectively. In order to statistically evaluate the quantity of energy transfer, we then calculate the integrated Wint during a certain time interval. In the simulation, the intense generated rising chorus waves propagate toward the positive h region and resonate with counter-streaming energetic electrons having negative parallel resonance velocity with respect to the ambient magnetic field direction. Although only electrons near a specific resonance velocity involve cyclotron resonance with whistler-mode waves, all electrons are used in the calculation of Wint.
The WPIA is a software function installed on the ERG satellite. In the WPIA calculation, we presented a processing method to reduce the errors of the wave phase in order to accurately evaluate the statistical significance of the energy transfer. The WPIA processing using the FFT and IFFT is costly. Moreover, the proposed overlapping processing of the waveform requires more computation time compared to that without overlapping. The computation resources (e.g., CPU clock, memory size, and bus width) are limited for the onboard data processing. We next address the evaluation of data processing speed and optimization of the software algorithm of the WPIA.
The target of the WPIA measurement is to evaluate the energy transfer between chorus waves and the resonant electrons. The ECH and MSW may affect particle motions. The particle fluctuations give uncertainty evaluation of Wint. From spectral information, we therefore avoid the WPIA calculation during a period that the ECH and MSW exist. In addition, considering the resonance condition between waves and particles, we can expect that the particle energies influenced by ECH and MSW are almost different from those interacting with chorus waves. We select the kinetic energy of electrons for the WPIA calculation by referring the cyclotron resonance condition with chorus waves. We are planning to use other information such as the plasma density for the evaluation of the resonance condition, by referring to the linear dispersion of the whistler wave mode. The influence of ECH and MSW waves on the WPIA measurement should be evaluated by a self-consistent multi-dimensional simulation and is left for the future study.
In the particle simulation, a coherent rising-tone element with the enhanced nonlinear wave growth () is formed after moderate linear wave growth of incoherent whistler-mode waves. The WPIA measurement demonstrated significant energy transfer from an energetic electron to a whistler-mode chorus wave which occurs during the generation of the coherent rising chorus element. During the period of in which the linear wave growth occurs near the frequency ω=0.2Ωe0, the WPIA measurements indicate the gradual increase of the quantity W, exceeding the 2 σw (Figure 10).
The main goal of the WPIA is to directly measure the quantity of energy transfer between whistler-mode chorus waves and resonating energetic electrons in the space plasma environment. In order to statistically evaluate the quantity of energy transfer, it is important to obtain accurate phase angles of the wave vector and the velocity vector of a particle. In addition to chorus waves, various other waves are included in the observed waveform, which affects the accuracy of the calculated quantity of energy transfer. The wave modes are removed through the passband filtering. However, the removed spectrum causes undesirable phase angle errors of the waveform. In order to reduce the phase errors, the overlapping processing is applied using an appropriate window function. The processing shows that the phase angle errors are improved successfully. The proposed waveform processing method is necessary in order to reduce the phase error and is applicable to the calculation of theWPIA.
This paper is dedicated to Prof. Takayuki Ono, who passed away on 21 December 2013. The computations in the present study were performed on the KDK system of RISH and ACCMS at Kyoto University. This work was supported by grant-in-aid 23224011 of the Ministry of Education, Culture, Sports, Science and Technology in Japan.
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