GPGPU acceleration of ISR plasma line analysis and
application to Arecibo plasma line striations
Nathaniel J. Hilliard , J. Vierinen , P. J. Erickson , M. P. Sulzer
1,2
2
2
3
njhilliard@wisc.edu
Department of Physics, University of Wisconsin – Madison, 2MIT Haystack Observatory, 3Arecibo Observatory
1
Introduction
Plasma Line
Incoherent scatter radar (ISR) returns
two primary resonances, the high
power, narrow band (~kHz) ionacoustic resonance and weaker
Langmuir
mode
(plasma
line)
resonance.

The ion-acoustic echo contains
information of plasma velocities,
electron and ion densities and
temperatures, and ion composition.

To obtain these accurately, a robust
scattering model is needed, containing
ambiguities in final fitted parameters.

Plasma line resonance measurements
provide an accurate electron plasma
frequency, containing absolute electron
density information, able to be used as
priors for the previous model.

Because the plasma lines occur at
frequencies 1 to 15 MHz outside the
central band and that they are very
narrow, high spectral resolution is
required.

In addition to informing the ionacoustic
models,
plasma
line
measurements include other previously
unexplained phenomena, such as white
power spectrum striations seen in
Figure 6.

s
GPGPU Acceleration
GPGPU
To sample well over this large range with the
requisite resolution, high computational power is
needed, especially for real-time monitoring.

General purpose computing on graphics
processing units (GPGPU) has the necessary
power for this highly parallelizeable task (element
calculations are independent of one another).

NVIDIA GPU's are the common choice for
scientific GPGPU implementation, and it is our
choice here, mainly due to its mature development
community and high-level CUDA C programming
language and extensions.

Figure 1: Performance comparison of various recent NVIDIA GPUs to Intel
CPUs in terms of raw floating point operations per second (FLOPS) for single
and double precision floats [NVIDIA Corporation, 2015].
3 k kb T e 2 2
f =f + 2
+ f c sin ( α)
4 π me
2
∑∑
TEMPLATE DESIGN © 2008
www.PosterPresentations.com
Fast Fourier Transforms
Range Step
Echo
CE
O
N2
Spectrum Accumulation
Transmit
Pulse
Time (t)
N2
+
HOST
Return
accumulated
spectrum.
Intermediate
Result
DEVICE
Accumulate
spectrum sum
over many pulses.
To process the data on the GPU, each transmit pulse and its
echo is copied into device memory, and processes, called
kernels, are run in succession.
●
First, the transmit pulse is complex multiplied with a section
of the echo, and this is stepped by the range gate size up to
the number of range gates. The intermediate is stored in
device memory.
●
Second, we use cuFFT, an optimized fast Fourier transform
(FFT) library, on each row of the intermediate result and
return results in place.
●
Finally, we add this intermediate to a spectrum result of the
same size, existing in device memory.
●
This allows us to loop outside of the kernels to process each
pulse and echo that we have in the host data, and finally copy
the spectrum result back to the host memory.
O+
e- e-
Superthermal
Electrons
●
Figure 5: Sharp extreme ultraviolet solar radiation (EUV)
impacts polar regions, ionizing neutrals. Freed electrons then
propagate with field-aligned motion, carrying velocities
matching the specific solar spectral feature energy minus the
requisite ionization energy of the neutral species. These
characteristic velocities underlie a corresponding resonance
frequency and energy, with relations described below, and give
rise to the spectral features seen on the right.
Figure 6: Selected plasma line power spectrum data from March 17 th, 2015 at
Arecibo for 75 degrees elevation. We include modeled locations of the power
striations corresponding to sharp spectral features in the field-aligned superthermal
electron populations at the energies specified. On the top, we mark approximate
pointing directions, north, west, south, and east. Aspect angle between radar
pointing and magnetic field direction are plotted on the bottom.
Superthermal electrons produced isotropically
at the poles move along the magnetic field lines
towards the opposite pole.
●
Electrons with low pitch angles will move
further along the field lines before interacting
and losing their energy characteristics, and we
can approximate them as follows:
●
Assuming the photoelectron component
perpendicular to the field line is close to zero,
v describes the component of velocity giving
rise to the plasma line enhancements:
●
Bandwidth(GB/s) Time(s) Speed Ratio Speedup
Intel i5-4660
N/A
120
0.008
1.00x
TESLA C2050
8.0
4.423
0.226
27.13x
GTX 970
8.0
2.530
0.395
47.43x
GTX TITAN
8.0
1.742
0.547
68.89x
EVGA GTX 780Ti SC
8.0
1.488
0.672
80.65x
Figure 2: Diagrammatic sketch (not to scale) of the thermal density fluctuations
(giving rise to the ISR range-Doppler spectrum) of the electrons in a collision-less
plasma over the entire frequency range. The exponential decrease should be much
more rapid and the ion-acoustic width shorter compared to the distance to the
plasma frequency [Dougherty and Farley, 1960].
Where fp is the plasma frequency, kb is
Boltzmann's constant, k is the
wavenumber, Te is the electron
iωt
mt =
ϵ t−r e σ r ,ω + ξt σ =N (0, S )
r,ω
ℂ
r,ω
ω
temperature, me is electron mass, fc is
r
1
2
electron gyro frequency (circular
4
H
−1 H
3
x ML =( A A ) A m
oscillation around magnetic field lines),
m= Ax + ξ
and α is the aspect angle between wave
6
H
5
H
vector and magnetic field.
x ML ≈ A m=x CE
A A≈α I
In our GPU code, we want the resultant power spectrum. We start above (1) with the measurement
equation giving the measured signal at time t. Here, εt-r is the transmit waveform; ω, its frequency;
σ, the received scatter; and ξ the environmental noise. Due to the incoherence of ISR scatter, the
return scatter (2) is a random complex number from a distribution centered at 0 with deviation of
power spectral density S, constant over each pulse. We rewrite this in linear form (3), then solve
for the maximum likelihood estimate xML with input experimental measurement m (4). With a
psuedo-random transmit pulse, we can simplify above to order identity (5), arriving with an
approximation for the correlation estimate (6), which, squared, gives us power: P=⟨|X |2 ⟩
EUV Photons
Complex Multiplication
Hardware
To analyze the plasma lines, we need to
process the echo over the entire range
spectrum (~30 MHz), shown (not to
scale) by Figure 2.ure
The plasma line resonance will be
located at an offset in frequency derived
by Yngvesson and Perkins, 1968:
2
p
DEVICE
Process one
transmit pulse and
echo at a time.
HOST
Includes many
transmit pulses
and their echoes.
Figure 3 (above): Visualization of the GPU processing algorithm developed, including a space-time diagram of the radar pulses.
Figure 4 (right): Displays how the GPU requires the data broken into small portions (blocks) that run in succession on each of the GPU's
processing banks (streaming multiprocessors). Each thread will performs one element-wise calculation.
Table 1 (below): Using a simulated data set for one second of ISR, we perform the analysis with various hardware. CPU processing was done
with multicore processing, though at a lower parallelization than that of the GPU algorithm. We compare the process time to data inflow rate to
obtain the speed ratio for performance metrics.
Plasma Line Analysis
2
r
Range
(=ct)
Plasma Line Striation Modeling
ν=⃗
ν ∥ ∘ ⃗k
●
As a result, plasma frequency matching the
Langmuir wave propagation in the radar
direction can be used to relate that plasma
frequency fr of the electron, with energy E, that
causes enhancement of the plasma resonance,
including a cosine term for projection to field
alignment and the radar pulse wavelength λ:
2
fr λ
1
E= m e (
)
2
cos θ 2
Figure 7 (below): The photoelectron velocity component aligned
with the radar pointing k. Langmuir waves propagating towards or
away from the monostatic radar will have Landau damping effects on
the velocity component aligned with the radar pointing,.
Conversely, we solve for resonance
frequency and then forward-model input
energies to match the striations seen in
Figure 6.
●
The energies modeled suggest specific solar
electronic transitions (He lines, etc.) giving
rise to the EUV rays and the resulting
specific-energy superthermal electrons.
●
The 50eV lines seen only in the western
sky support this; local time is close to
sunset, only providing superthermal
electron production in the western region.
●
Conclusion
Acknowledgements
The GPU algorithm developed here conveys order-of-magnitude speedup over traditional
CPU processing.
●
Our algorithm does not present the limit to GPU analysis, and additional speedup may be
found, with possible avenues: (1) decreasing block sizes and using shared memory with
strided thread computation; (2) asynchronous pinned host memory transfers, occurring
during kernel executions; (3) dynamically reducing echo size to only transfer the needed
elements.
●
With further optimization of the algorithm here and the speed advancements seen in Figure
1, a single GPU solution for real-time analysis nearly within reach.
●
Field aligned scans show stark plasma line power striations due to solar UV photons
imparting characteristic energies to electrons moving along the field lines.
●
Plasma line power striation measurements provide a remote, ground-based effective
spectrometer for studying solar EUV output and its effects on the near-space environment.
Arecibo plasma line data and analysis base code supplied by Mike Sulzer. Special thanks to
MIT Haystack Observatory for the project support, including technical expertise, facilities, and
hardware. Extra special thanks to project mentors Juha Vierinen and Philip Erickson for their
direction and guidance during project development. This was made possible by the NSF
Research Experiences for Undergraduates grant AST-1156504 to MIT Haystack Observatory.
●
Selected References
Dougherty, J. P., and D. T. Farley (1960), A Theory of Incoherent Scattering of Radio Waves by a Plasma,
Proceedings of the Royal Society of London. Series A, 259, 79.
NVIDIA Corporation (2015), CUDA Programming Guide Version 7.0
Yngvesson, K., and F. Perkins (1968), Radar thomson scatter studies of photoelectrons in the ionosphere and
landau damping, Journal of Geophysical Research, 73 (1), 97–110.