The software-type wave–particle interaction analyzer (S-WPIA) is an instrument package onboard the Arase satel- lite, which studies the magnetosphere. The S-WPIA represents a new method for directly observing wave–particle interactions onboard a spacecraft in a space plasma environment. The main objective of the S-WPIA is to quantita- tively detect wave–particle interactions associated with whistler-mode chorus emissions and electrons over a wide energy range (from several keV to several MeV ). The quantity of energy exchanges between waves and particles can be represented as the inner product of the wave electric-field vector and the particle velocity vector. The S-WPIA requires accurate measurement of the phase difference between wave and particle gyration. The leading edge of the S-WPIA system allows us to collect comprehensive information, including the detection time, energy, and incoming direction of individual particles and instantaneous-wave electric and magnetic fields, at a high sampling rate. All the collected particle and waveform data are stored in the onboard large-volume data storage. The S-WPIA executes cal- culations asynchronously using the collected electric and magnetic wave data, data acquired from multiple particle instruments, and ambient magnetic-field data. The S-WPIA has the role of handling large amounts of raw data that are dedicated to calculations of the S-WPIA. Then, the results are transferred to the ground station. This paper describes the design of the S-WPIA and its calculations in detail, as implemented onboard Arase. Keywords: Wave–particle interaction, Onboard processing, Inner magnetosphere Adiabatic acceleration, which involves the process of Introduction radial diffusion, is referred to as an external-source accel - Radiation belts are composed of inner and outer belts, eration (Hudson et al. 2001; Elkington et al. 2003; Shprits and highly relativistic electrons are trapped in the outer et al. 2008), and local acceleration, which involves wave– belt. The structure of the inner belt is relatively sta - particle interactions, is known as an internal-source ble, while in the outer belt, the electron flux drastically acceleration (Miyoshi et al. 2003; Thorne et al. 2013; changes during magnetic storms. These fluxes show Reeves et al. 2013). Whistler-mode chorus waves, which sudden increases and decreases during the main and are frequently observed outside the plasmasphere (e.g., recovery phases of storms (Baker et al. 1986; Blake et al. Santolik et al. 2003; Li et al. 2009), are considered pos- 2001; Reeves et al. 2003). Two sources of particle accel- sible causes of particle acceleration to relativistic ener- eration have been proposed (Green and Kivelson 2004). gies in the inner magnetosphere during magnetic storms (Summers et al. 1998; Meredith et al. 2002). The energy of particles trapped in the wave potential of coherent *Correspondence: firstname.lastname@example.org Institute of Space and Astronautical Science, Japan Aerospace whistler-mode waves could be efficiently increased to Exploration Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa relativistic energies in the order of magnitude of several 252-5210, Japan MeV (Omura et al. 2007; Summers and Omura 2007). Full list of author information is available at the end of the article © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creat iveco mmons .org/licen ses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Hikishima et al. Earth, Planets and Space (2018) 70:80 Page 2 of 12 The Arase (ERG: Exploration of Energization and Radia - N N tion in Geospace) satellite was launched by the Japan 1 σ = (qE (t ) · v ) − qE (t ) · v , w w i i w i i Aerospace Exploration Agency on December 20, 2016. i=1 i=1 Its primary mission is to study particle acceleration pro- cesses in geospace (Miyoshi et al. 2013; Miyoshi et al. (2) submitted to Earth, Planets, and Space). The Arase car - where N is the total number of particles, v is the velocity ries the software-type wave–particle interaction analyzer of the ith particle detected at time t , and E denotes the i w (S-WPIA) instrument package and processing applica- wave electric field. tion. The S-WPIA directly measures the local energy exchange through resonant interactions between the SWPIA in ‑ the Arase satellite system plasma waves and electrons in the inner magnetosphere. Mission network and components associated with SWPIA ‑ The fundamental concept of the WPIA is described by The Arase’s mission system has two sets of Mission Data Fukuhara et al. (2009). They designed the method as a Processor (MDP)/Recorder (MDR) units. Both MDP/ One-chip WPIA (O-WPIA), using an onboard field- MDR#1 and #2 are completely identical with respect to programmable gate array (FPGA). The WPIA computes their designs and functions. They are interchangeable the kinetic energy variation of a plasma particle over and provide redundancy for data processing and stor- time, using the physical quantities of waves and particles age (Takashima et al. 2018). The S-WPIA runs on the acquired by onboard instruments. To validate the calcu- MDR, which is an onboard digital processing unit with lation method of the WPIA, plasma-particle simulations a flash memory of 32 GB. The flash memory is used as a were performed to verify the resonant interaction of data recorder dedicated to data storage for the S-WPIA. whistler-mode chorus waves and energetic electrons. The The S-WPIA processes data stored on the flash memory pseudo-measurement of the WPIA statistically indicated of the MDR from the following instruments (hereafter that there was a significant transfer of energy, exceeding referred to as “cooperative instruments”) for measuring the standard deviation (Katoh et al. 2013; Hikishima et al. waves, particles, and the ambient magnetic field: 2014). In the Arase satellite, the calculation method of the WPIA is implemented through the S-WPIA, which • PWE: WaveForm Capture (WFC) receivers of Plasma functions using software. The S-WPIA approach pro - Wave Experiment (Kasahara et al. 2018b) vides flexibility for the calculations, including alternative • MEP-e: Medium-Energy Particle Experiment—Elec- calculation modes, variable parameter settings, calcula- tron Analyzer (Kasahara et al. 2018a) tions for other wave modes, and software updates. In this • HEP-L and HEP-H: High-Energy Electron Experi- study, we present the functional design and specifications ments with low- and high-energy measurements, of the S-WPIA implemented onboard the Arase satellite. respectively (Mitani et al. submitted to Earth, Plan- ets, and Space) Principle of Wave–Particle Interaction Analyzer • XEP: Extremely High-Energy Electron Experiment The fundamental concept of the WPIA is described by (Higashio et al. submitted to Earth, Planets, and Fukuhara et al. (2009) and Katoh et al. (2013). The WPIA Space) requires instantaneous-wave field vectors and velocity • MGF: Magnetic Field Experiment (Matsuoka et al. vectors of incoming plasma particles. The quantity W, 2018). the time variation of the kinetic energy K of a charged particle, is represented by the inner product of the wave Figure 1 shows the configuration of the mission network. electric field E and particle velocity v as follows: Note that the figure covers only the cooperative instru - ments and other components that are related to the oper- dK d(γ v) ation of the S-WPIA. Table 1 gives the specifications for W = = m v · = qE · v , 0 (1) dt dt the above cooperative instruments. The observation data where K = m c (γ − 1) , m is the particle rest mass, c is are transferred from the instruments to the flash memory 0 0 the speed of light, γ is the Lorentz factor represented by of the MDR via the mission network (Takashima et al. −1/2 2018). The S-WPIA executes calculations using the data 1 − (v/c) , and q is the particle charge. The sign of stored in the flash memory of the MDR. W indicates wave damping/particle acceleration (posi- The S-WPIA executes the functions listed below and tive) or wave growth/particle deceleration (negative). We controls MDR functions in addition to performing calcu- statistically evaluate the magnitude of the energy transfer lations in the S-WPIA. by summing W over a given time interval. The statistical significance is evaluated using the standard deviation σ (Katoh et al. 2013) as follows: Hikishima et al. Earth, Planets and Space (2018) 70:80 Page 3 of 12 1 Issuing directives to the cooperative instruments to the output of the S-WPIA. The S-WPIA reads the raw control the starting and stopping of data generation. data from the flash memory and performs calculations 2 Executing calculations in the S-WPIA calculations according to the algorithm of the S-WPIA. The pro - and writing both calculation results and raw data to cessed data are losslessly compressed by a range encod- flash memory. ing method (Martin 1979), and the compressed data are 3 Transferring PWE burst data (Kasahara et al. 2018b; written back to the flash memory. Matsuda et al. 2018) from the MDR to the System The PWE burst data are the five components of con - Data Recorder (SDR) of the satellite bus system. tinuous electric-field and magnetic-field waveform data written into the flash memory of the MDR during a spe - Data recorder for SWPIA ‑ cific observation time period via the mission network Figure 2 shows the configuration of the MDR and the under the control of the PWE. The burst data allow us cooperative instruments. The MDR flash memory is par - to perform detailed data analyses, such as determin- titioned into two broad areas, one for storing data for the ing polarizations and Poynting fluxes. Details pertaining S-WPIA (both raw and processed data) and the other to the PWE burst data are reported by Kasahara et al. for storing PWE burst data, as shown in Table 2. The (2018b). raw data are unprocessed data that are recorded directly by the cooperative instruments. The processed data are Table 1 Data specifications for the S ‑ WPIA Instruments Components Data Range Resolution PWE E , E Waveforms 10 Hz–20 kHz/120 kHz 65,536 Hz/262,144 Hz x y B , B , B Waveforms 10 Hz–20 kHz 65,536 Hz x y z MEP-e Energy 7–87 keV 1.9μs HEP HEP-L Energy 70k–1 MeV 1.9μs HEP-H Energy 700k–2 MeV XEP Energy 400k–20 MeV 1.9μs Fig. 1 Configuration of the mission network for S-WPIA. The MDP/MDR and CPU boards of scientific instruments (XEP, HEP, MEP-e, PWE, and MGF) related to the S-WPIA connect with the mission network. The instruments write raw data for the S-WPIA to the MDR through the mission network. The S-WPIA clock and the reset pulse are then transferred from the PWE to the FPGA of the particle instruments through leased lines Hikishima et al. Earth, Planets and Space (2018) 70:80 Page 4 of 12 Table 2 Partition assignments in the MDR Data generation mode of SWPIA ‑ With the exception of the MGF, each cooperative instru- Instruments Content Size (GB) ment adds a flag to the relay packet when it is ready to PWE Burst data (16 partitions: E/B waveforms) 13 transmit its own data, while the MGF is constantly trans- S-WPIA Raw data (7 partitions: XEP, HEP-L/H, MEP-e, 6 mitting its data via the relay packet. The S-WPIA has two PWE-E/B, MGF) independent observation modes: Processed data (12 partitions) 12 Nominal mode The nominal mode is a simple data generation operation. Time tag in SWPIA sy ‑ stem When the S-WPIA receives a command from the ground To meet the scientific objectives of the S-WPIA, the rela - or a satellite system (scheduled at a specified time), it tive time precision between the plasma wave data and transmits a generation flag via the relay packet. The flag particle data must be less than 10μs (Katoh et al. 2018). identifies the cooperative instruments that should be This precision is maintained by two time-keeping sys - activated for data generation (any combination of wave tems: (1) the 64 Hz time index (TI) distributed by the and particle instruments can be selected). Each coopera- onboard satellite system and (2) the 524,288 Hz S-WPIA tive instrument looks for its own flag in the relay packet. clock distributed by the PWE (Fig. 1). Each cooperative Once an instrument receives its data generation flag, it instrument has a 24 bit S-WPIA clock counter, which adds an “answer back” flag to the relay packet and begins incrementally advances the distributed S-WPIA clock. to generate raw data, which are stored in the MDR par- As a result, the S-WPIA clock counter has a time preci tition (Fig. 2). During data transmission, the instrument sion of 1.9μs . The S-WPIA clock counter is reset by the adds a flag indicating the state of the data transmission. reset pulse distributed by the PWE. Because the S-WPIA clock is generated by the same source clock as that used Trigger mode to sample waveforms in the PWE, the S-WPIA clock The trigger mode is prepared for acquiring targeted data counter is synchronized to the sampling of plasma wave effectively. In the trigger mode, the cooperative instru - data. Regarding the particle instruments, the detec ments continue to write their observation data into the tion time for each particle is not synchronized with the MDR until they receive the command to stop the data S-WPIA clock counter, so each instrument applies a time generation. Each partition of the MDR is formed as a tag with the latest S-WPIA clock counter to each particle kind of a ring buffer, and the stored data are automatically detection. The precision of the relative time between data overwritten. The PWE computes the spectral intensities acquisitions for plasma waves and particles is 1.9μs . The of the wave magnetic field at four different frequency observation time of the S-WPIA is defined by combining bands. The frequency bands correspond to the band for the TI and S-WPIA clock counters. the upper-band chorus, lower-band chorus, hiss, and magnetosonic wave. The PWE computes spectral inten - Data sharing through the mission network sities in each band with respect to the magnitude of the The instruments that are connected through the mis - ambient magnetic field that is distributed onboard and sion network communicate with each other using spe- includes them on the relay packet. They are used by the cial communication packets called “relay packets.” The S-WPIA as the trigger signal. Once the spectral intensity S-WPIA also uses relay packets to communicate with that is selected from among the four frequency bands each cooperative instrument. The relay packet circulates exceeds the threshold level, the S-WPIA records the TI through the network at a cycle of 1 s. With respect to and the status of other necessary flags, and deactivates the operation of the S-WPIA, the relay packet contains the cooperative instruments at a specific time after the control flags that are used for activating or deactivating trigger detection. The start time for the data to be pro - the data generation in each cooperative instrument. In cessed by the S-WPIA is determined by referring to the addition, the relay packet contains the magnitudes of the observed spectral intensities provided by the PWE. ambient magnetic field observed by the MGF, and inte grated wave-spectrum intensities are used for the trigger- Data processing algorithm mode operation of the S-WPIA and the electron plasma In this section, the onboard processing of the S-WPIA density data (Kumamoto et al. 2018) from the PWE. Data is described in detail. The S-WPIA has two main func - from the MGF are used for coordinate conversion in the tions: perform calculations according to the algorithm of S-WPIA. the S-WPIA and perform a data dump from the MDR to the SDR. During the data dump, the S-WPIA transfers the raw data generated by the cooperative instruments, Hikishima et al. Earth, Planets and Space (2018) 70:80 Page 5 of 12 MD MDP P / MD / MDR R PW PWE E SDRA SDRAM M SD SDR R XE XEP P S-WPIA S-WPIA application application HE HEP P MEP-e MEP-e Flash memory Flash memory PW PWE E Burst Burst data data S-WPIA S-WPIA Processed Processed dat data a S-WPIA S-WPIA Raw data Raw data Fig. 2 Configuration of the MDR and the cooperative instruments. The application of the S-WPIA commands each instrument to generate data for the S-WPIA using a generation flag. Then, each instrument sends raw data to the flash memory. The application executes the calculations using the raw data. The results are sent back to the flash memory as processed data stored in the raw data partition, to the SDR. The compu - where E denotes the wave electric field and t is the w i tational results of the S-WPIA stored in the processed detection time for each particle. In addition, the S-WPIA partition and the PWE burst data stored in the PWE par- computes B · v related to the frequency variation of tition of the MDR are also transferred to the SDR. Since chorus emissions (Omura and Nunn 2011). The result the S-WPIA processing requires considerable computa- for W is output in the form of three-dimensional (3D) int tion time, the S-WPIA prioritizes the data dump process arrays of W , comprising components of kinetic energy int over the calculation process. Once the data dump starts, K, pitch angle α , and phase difference ζ , which denotes the calculation process of the S-WPIA is interrupted, the phase difference between the wave magnetic-field resuming automatically after the data dump ends. vector and the velocity vector of the particle on the per- pendicular plane with respect to the ambient magnetic Overview of processing in SWPIA ‑ field. Figure 3 shows the main flow of S-WPIA processing. The S-WPIA requires the input of waveforms: two The S-WPIA computes physical quantities that express components of electric fields, detected by two pairs of the energy exchange between waves and particles. As wire probe antennae, which are extended on the spin described in the previous section, the energy exchange plane of the spacecraft (Kasahara et al. 2018b), and three is represented as the inner product of the electric-wave components of magnetic fields, detected by triaxial field vector E and the individual particle velocity vector v. search-coil magnetometers (Kasahara et al. 2018b; Ozaki The integrated quantities W during time interval t are et al. 2018). The signals that are detected by these sensors int computed as follows: are passed through several bandpass filters and variable- gain amplifiers. The observed waveform data contain the effects of phase distortion as well as the effects of the W = qE (t ) · v , int w i i (3) gain of the PWE receiver. The calibration process for the i=1 plasma wave observation is crucial because precise phase Data generatio Data generation/ n/ Answer bac Answer back k Raw Raw data data / Calculation / Calculation result results s Hikishima et al. Earth, Planets and Space (2018) 70:80 Page 6 of 12 read from the raw data partition to the onboard SDRAM WAVE E , E , B , B , B 1 2 1 2 3 memory before the calculations. PARTICLE FFT Calibration IFFT Processing of wave data Coordinate conversion One record of waveform data for the S-WPIA contains External magnetic field the TI, S-WPIA clock counter, data status, and 512 points of electric-field and magnetic-field waveform data. The time interval for one record corresponds to 7.8 ms in the nominal mode for a sampling frequency equal to 65,536 Hz. The S-WPIA clock counter represents the timing of the first data point. The data status contains informa - Fig. 3 Main flow of processing in S-WPIA tion about the operation mode of the PWE, such as the receiver gain and observation frequency bands. and amplitude data are essential for quantitative analyses Transfer functions for wave calibration of the S-WPIA data. The S-WPIA requires end-to-end transfer functions for To obtain the amplitudes and phases of plasma waves the WFC receivers, including the sensors needed to cali- detected by the sensors, the calibration process is per- brate the observed data. The transfer function for the formed in the frequency domain. After applying a fast magnetic-field data of the WFC is provided by the PWE Fourier transform (FFT) to the output signals of the PWE team, based on the results of testing on the ground. With receivers, the wave amplitudes and phases are calibrated respect to the transfer functions of the electric-field data according to the transfer functions of the PWE receivers. of the WFC, the antenna impedance needs to be consid- After the correction of the amplitude and phase, time- ered in addition to the calibration of the WFC receiver. series waveforms are obtained through an inverse FFT The impedance of the electric-field antennae depends (IFFT). Since the S-WPIA independently evaluates physi- on plasma density and temperatures, which means that cal quantities in the parallel and perpendicular directions the antenna impedance varies along the path of the satel- relative to the ambient magnetic field, the acquired elec - lite’s orbit. Depending on the location of the satellite, the tric and magnetic waveforms and particle data are con- S-WPIA can select the antenna impedance to be used in verted to vectors with respect to the ambient magnetic the calibration from among the typical impedance values field. The calculations of the S-WPIA are applied to the that are registered in advance. The PWE has the function above converted physical values. of measuring the antenna impedance by the onboard cal- ibration system (Kasahara et al. 2018b). The results of the SWPIA pr ‑ ocessing antenna impedance measurements provide the registered Figure 4 shows the calculation flow of the S-WPIA. values in the S-WPIA. Before starting the calculation, the tables needed to cali- The PWE has various operation modes. The gains and brate the data of the cooperative instruments are loaded observation frequency ranges of the receivers are control- in advance from the ground by specific commands. The lable by the telemetry commands and the onboard PWE functions of the S-WPIA are flexible. The commands software. The S-WPIA needs to perform the onboard cali - from the ground control the initial settings of the calcu- bration in consideration of the PWE operation modes. lations, such as the number of data points used in FFT Onboard preparation of the calibration tables for every and the frequency bandwidth of plasma wave data. The PWE operation mode is not realistic; therefore, the S-WPIA S-WPIA can also choose various combinations from reproduces the transfer function for each PWE operation among the cooperative instruments that are dedicated to mode using a cubic spline interpolation in Eq. (4). the calculations. The time period of the raw data used in the S-WPIA 3 2 S (x) = a (x − x ) + b (x − x ) + c (x − x ) j j j j j j j calculations is specified by the TI, which is also sent from (4) + d (j = 0, 1, ..., M − 1; x < x < x ) . the ground. Since the buffer size of the onboard syn - j j j+1 chronous dynamic random-access memory (SDRAM) where S (x) is the transfer function as a function of the fre- should be smaller than the size of the specified raw data, quency x on an interval [x , x ], x is the jth frequency at j j+1 j the S-WPIA reads the data from the raw data partition which the calibration data are available, a , b , c , and d are j j j j for time periods that are shorter than the targeted time the coefficients of the polynomials obtained by the cubic period. The duration of the read time is 10 s for parti - spline interpolation, and M is the number of data points of cle data and 1 s for wave data. Since the MGF provides the calibration table. data that are sampled at a lower rate, all of its data are Hikishima et al. Earth, Planets and Space (2018) 70:80 Page 7 of 12 Start Preparation MDR Read MGF data (Raw data) Upload tables for calibration i= 0 TI = Start TI Initialization TI =TI + ΔTI i+1 i (ΔTI=10 s) Set parameters Finish Yes TI > End TI calculation No Data handling (Waves, particles) Read MEP-e data Calculation Search event data of particle B Search wave data Next particle instrument MEP-e→ HEP-L→ Search MGF data HEP-H→ XEP C Convert coordinate ΣW, σ , N Data handling (Waves) MDR D Calculation of W, σ (Processed data) No Process all Yes Data handling particle data ? (Particles) Time tag of the particle data Yes > No End time of the plasma wave data Read wave data Data handling (1 s length) FFT Does dataexist Yes in SDRAM ? Passband filtering No Does data exist No Calibration i = i+ 1 in flash memory ? Yes IFFT Read wave data Return MDR (Raw data) Read particle data MDR (Processed data) Return Fig. 4 Overall calculation flow in S-WPIA Hikishima et al. Earth, Planets and Space (2018) 70:80 Page 8 of 12 Calibration particle data.) In addition, for wave processing such as The S-WPIA requires the onboard calibration of wave - FFT and calibration, large-size buffers are required on form data. The calibration of both wave amplitudes and the SDRAM. Since the data size of the MGF is relatively phases is carried out in the frequency domain. First, the small, all of the data generated during the calculation are S-WPIA converts the five components of observed wave - stored into the SDRAM. forms (two components of the wave electric field and The wave data size that the PWE produces per unit three components of the wave magnetic field) to com - time is constant and is determined by the sampling fre- plex spectra in the frequency domain using the complex quency, while the particle data vary depending on the FFT. The S-WPIA calibrates the obtained complex spec - intensity of the electron flux in the magnetosphere. The tra with respect to the reproduced transfer functions and maximum production size of the particle data is limited converts the calibrated complex spectra to waveforms by the data transmission bandwidth of the internal net- in the time domain using the inverse FFT. The FFT cal - work. During the processing of the S-WPIA, while read- culation is conducted for a frame containing a specific ing from the flash memory, the wave data are allocated on number of data points of the waveform. Its default num- the SDRAM for each 1 s of data, while the particle data ber is 512, which can be changed using telemetry com- are allocated for each 10 s of data. The algorithm always mands. The calibration process is repeated in the frame checks the start/end time (given by the set of containing of the FFT calculation. Since the continuity of the cali- the TI and S-WPIA clock) of WFC data allocated on the brated waveforms in consecutive FFT frames is crucial to SDRAM buffer. During the S-WPIA processing, when the S-WPIA, the S-WPIA applies window functions and the time tag of a particle-event data exceeds the end time frame overlapping to waveform data in the time domain. of a wave dataset, it then shifts to the processing of the A detailed description is reported in Hikishima et al. next particle instrument dataset. When there are no par- (2014). ticle datasets in the buffer, a new dataset is transferred from the MDR partition to the SDRAM buffer. The raw Processing of particle data data used in the calculations are compressed and sent to At the start of the calculations of the S-WPIA, data from the flash memory of the MDR as processed data to vali - the specified particle instruments are transferred to the date the calculation results on the ground. The handling SDRAM from each instrument’s assigned partition on of this data is managed using a flag set by the perform - the MDR. The sizes of the particle buffers in the SDRAM ing calculations. When there are no data in the MDR, are decided based on the assigned network bandwidth of the calculations for the instrument are excluded from the each particle instrument. A packet of particle data com- calculation sequence (controlled by the flag). When there monly consists of a TI packet, event packet, and coun- are no more particle data on the SDRAM within the ter-event packet. The TI packet is produced each time time range of the allocated wave data of SDRAM, then the S-WPIA clock counter is reset. The event packet new wave data are transferred into the SDRAM from the is produced every time a single particle is detected and MDR. includes information on the S-WPIA clock counter at the time of particle detection, such as the energy and Computation of W arrival direction of a particle. The counter-event packet The S-WPIA calculates E · v , B · v , and σ using the w w w is produced every 250 ms and includes the number of wave and particle datasets for the specified time span. particle detections that are not transferred to the MDR, The calculation procedure of the S-WPIA is as follows: due to high particle count rates. The S-WPIA identifies the observation time of each particle using both TI and 1. The S-WPIA extracts the S-WPIA clock counter, the S-WPIA clock counter that is included in the event energy, and arrival direction of a particle from each packet. Furthermore, the correction of the known time event packet. Then, the observation time of each delay between each sensor and its electronic circuit particle is determined by combining the TI in the TI is considered. Each instrument has a quality flag in the packet with the S-WPIA clock counter in the event event packet. The S-WPIA ignores the event packet when packet. The S-WPIA processes the particle data in the quality flag shows bad-quality data. the following order: MEP-e, HEP-L, HEP-H, and XEP. (process A in Fig. 4) Data handling 2. The S-WPIA searches the plasma wave data and The use of multiple instruments increases the complex - MGF data by referring to the observation time of ity of data handling. First of all, the data sizes between each particle. Because the time of detection of the waves and particles are largely different. (The wave data particle is not synchronized with the sampling of the size is approximately 10 times larger than that of the waveforms, the S-WPIA interpolates the waveforms Hikishima et al. Earth, Planets and Space (2018) 70:80 Page 9 of 12 at the time tag of the particle. The interpolation is The time interval can be set arbitrarily using commands also applied to the MGF data to obtain an instantane- and is typically shorter than the time scale (typically ous background magnetic-field vector. (process B) 100 ms) of the frequency variation of a chorus element. 3. Since the electric-field sensor along the spin axis This improves the signal-to-noise ratio of the S-WPIA is not equipped in the Arase satellite (see Kasahara because the frequency variation changes the energy and et al. 2018b), the S-WPIA computes the third com- pitch angle ranges of electrons, satisfying the cyclotron ponent of the wave electric-field vector oriented to resonance condition. the spin axis ( E ), using the relation E · B = 0 z w w under the assumption that the electromagnetic wave Verification of W calculation algorithm arrives from one direction. (process C) Katoh et al. (2013) demonstrated the validity of the cal- 4. The W = E · v , B · v , pitch angle α , and phase dif- culation method in the WPIA by conducting pseudo- w w ference ζ are calculated for each individual particle. calculations of the WPIA using the data obtained by Details of the calculations are described below. (pro- the particle simulations that represent the resonance cess D). between whistler-mode chorus waves and energetic elec- trons. The simulation was a one-dimensional (1D) elec - tron-hybrid code with a dipole magnetic field near the The S-WPIA calculates the quantities of the parallel and magnetic equator. The times for the wave fields and parti - perpendicular wave components with respect to the cle velocities were represented as discrete time steps. The ambient magnetic field B by the following procedure. accumulated W (Eq. 3) showed a negative value exceed- The parallel and perpendicular components of the wave int ing the standard deviation σ (Eq. 2) during the genera- electric-field vector ( E , E ) can be expressed by w w⊥ w tion of whistle-mode chorus elements. The variation in E = (E · e ) e , w� w B B 0 0 W represented the energy transfer from particles to int (5) E = E − E , w⊥ w w� waves. To verify the validity of the S-WPIA implemented where e is the unit vector of B . The parallel and per - B 0 onboard the Arase, we calculated W and σ through pendicular components of both the wave magnetic-field int w the onboard S-WPIA software, using the simulation data vector ( B , B ) and velocity vector ( v , v ) are obtained w w⊥ ⊥ obtained by Katoh et al. (2013) instead of the observation by the same procedure. The pitch angle α is given by data acquired by the Arase. The time resolution of a time v · e = |v| ·|e | cos α , B B 0 0 (6) tag in the simulation is constant because the simulation advances waves and particles in each discretized time v · e −1 0 α = cos . step. The algorithm of the S-WPIA is executed by refer - (7) |v| ·|e | ring the time tag. With respect to the time tag of indi- vidual particles in the simulation data, we calculated and The arccosine is obtained by referring to a conversion accumulated W using wave fields with corresponding table, without the use of mathematical operations. The timing. The calculation results generated by the onboard phase difference ζ between v and B is obtained by ⊥ w⊥ S-WPIA and by Katoh et al. (2013) are shown in Fig. 5. In B · v =|B |·|v | cosζ , w⊥ ⊥ w⊥ ⊥ (8) the same manner as the simulation, particles with a pitch ◦ ◦ angle of 100 –110 and energy values ranging from 200 B · v w⊥ ⊥ −1 to 400 keV were used in the S-WPIA. The resolution of ζ ζ = cos . (9) |B | ·|v | w⊥ ⊥ was 15 in the simulation, whereas the minimum resolu- ◦ ◦ ◦ tion of ζ in the onboard S-WPIA is 30 . The results of the Since ζ is defined from 0 to 360 , we refer to the sign of time variation W of integrated E · v and the ζ distribu- int w (B × v ) · e w⊥ ⊥ B 0 (10) tion obtained by the S-WPIA show good agreement with those from the simulation obtained by Katoh et al. (2013). to determine the corresponding quadrant. The S-WPIA This agreement denotes that the onboard S-WPIA soft - collects the integrated data described above for each ware correctly works on the Arase. particle instrument, stores the data with an embedded header describing the integration and compression, and Optional processing then transfers the data to the processed data partition of The S-WPIA is equipped with some optional processing the MDR. modes to improve the statistical significance of its output. These quantities are integrated over a specific time Chorus emissions are characterized by narrowband interval (10 ms) in the form of 3D arrays W (K , α, ζ) , int spectra with rising or falling frequency tones over time. σ (K , α, ζ) , and N (K , α, ζ) to obtain the particle count. w Hikishima et al. Earth, Planets and Space (2018) 70:80 Page 10 of 12 Other emissions (e.g., electron cyclotron harmonic where ω is the wave frequency, is the local electron waves, MSWs) appear with the chorus waves. When this gyrofrequency, and k is the parallel component of the happens, the waveform of chorus elements to be ana- wave number of whistler-mode waves, given by lyzed by the S-WPIA is contaminated. Since the contami- nation reduces the statistical significance of the S-WPIA 2 ω pe k = 1 + , (12) output, a spectral extraction method is applied to remove c ω(� − ω) the other emissions. During the calibration procedure for wave electromagnetic fields, after passband processing where ω is the electron plasma frequency. During the pe with fixed frequencies, the most intense spectral compo - computation of resonance velocity, the wave frequency nent and the adjacent two components are used to recon- of the dominant mode is used, which is obtained in the struct the calibrated waveform. The other frequency FFT analysis for a time interval during which the cho- components are set to zero. An appropriate frequency rus frequency does not vary largely over time. Since ω pe resolution and a window function are selected for the is needed to compute the resonance velocity, we refer to spectral extraction. the upper hybrid resonance frequency ( ω ) provide d UHR To improve the signal-to-noise ratio of the S-WPIA by the PWE high-frequency analyzer (Kumamoto et al. output, we can focus on particles with kinetic energies 2018) every second via the relay packet. The plasma fre - and pitch angles that satisfy the cyclotron resonance con- quency can be obtained from dition in chorus emissions. The resonance velocity V 2 2 2 for waves propagating purely parallel to the background ω = ω + � . (13) UHR pe e magnetic field is given by With respect to the computed resonance velocity, we can ω − � /γ V = , select particles that satisfy the resonant condition with (11) ab Fig. 5 Calculation results of W and ζ distribution. (top) Time variation of W . The solid line indicates the W and the dashed lines indicate int int int W ± 1.96σ . (bottom) ζ distribution. a Calculation results using the algorithm of the S-WPIA. b Simulation results from Figs. 4a and 5a in Katoh int w et al. (2013) Hikishima et al. Earth, Planets and Space (2018) 70:80 Page 11 of 12 implement the S-WPIA. KA and TT managed the overall mission system to the observed chorus elements for the calculations of the acquire the data. All authors read and approved the final manuscript. S-WPIA. In the nominal observation mode, the PWE captures Author details Institute of Space and Astronautical Science, Japan Aerospace Explora- waveforms at a sampling frequency of 65 kHz. A higher tion Agency, 3-1-1 Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, sampling frequency of 120 kHz is available only for the Japan. Research Institute for Sustainable Humanosphere, Kyoto University, wave electric field to obtain the amplitude and phase of Gokasho, Uji, Kyoto 611-0011, Japan. Department of Geophysics, Graduate School of Science, Tohoku University, 6-3 Aramaki-aza-aoba, Aoba, Sendai, the waveform with better time resolution. At this higher Miyagi 980-8578, Japan. Graduate School of Natural Science and Technology, sampling rate, the waveform is intermittently transferred Kanazawa University, Kakuma, Kanazawa, Ishikawa 920-1192, Japan. School to the MDR due to the assignment of the transmission of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan. Japan Aerospace Exploration Agency, 2-1-1 Sengen, Tsukuba, Ibaraki band. The frequency resolution of the spectra is deter - 305-8505, Japan. Institute for Space-Earth Environmental Research, Nagoya mined by the number of data points used in the S-WPIA University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8601, Japan. Osaka calculation, and this number is automatically adjusted to University, Toyonaka, Osaka 560-0043, Japan. match the frequency resolution of the 65 kHz sampling Acknowledgements mode. The authors express their sincere gratitude for the significant contributions made by all members of the ERG project. This study is supported by Grants- in-Aid for Scientific Research (17H06140, 16H06286, 15H05815, 15H05747, Conclusions and 15K17771) of the Japan Society for the Promotion of Science. This work In this paper, a detailed design of the application of the was carried out as a joint research program with the Institute for Space-Earth S-WPIA onboard the Arase satellite to the exploration Environmental Research (ISEE), Nagoya University. The authors wish to thank the late Professor Takayuki Ono for his valuable discussions and continuous of wave–particle interactions in the magnetosphere is encouragement during this study. described. The basic purpose of the WPIA is to measure the energy transfer between plasma waves and charged Competing interests The authors declare that they have no competing interests. particles. The application is installed in the onboard MDP/MDR#1 and #2, which have a large memory of 32 Availability of data and materials GB for storing high-resolution data. The application col - Not applicable. lects the wave electric- and magnetic-field waveforms Ethics approval and consent to participate that are sampled at 65 kHz using the PWE; raw data of Not applicable. individual detected particles are provided by MEP-e, HEP-L/H, and XEP, and the background magnetic-field Publisher’s note data are measured by the MGF. Each instrument moni- Springer Nature remains neutral with regard to jurisdictional claims in pub- lished maps and institutional affiliations. tors the relay packet traveling through the system net- work and generates a dataset dedicated to the S-WPIA Received: 7 September 2017 Accepted: 1 May 2018 when the appropriate flag generated by the S-WPIA is detected. Data for the S-WPIA are stored on the MDR, and data processing begins when the S-WPIA receives a command specifying the time interval of the subject to References be applied to the calculations of the S-WPIA. The cal - Baker DN, Blake JB, Klebesadel RW, Higbie PR (1986) Highly relativistic culation process includes FFT, IFFT, bandpass-filtering, electrons in the Earths outer magnetosphere: 1. Lifetimes and temporal data search, interpolation, and coordinate conversion. history 1979–1984. 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