# Presentation: 702521

## Electron Polar Cap Density Profiles Using the IMAGE Radio Plasma Imager

- Aramis Martinez, Vance Henize, Patricia Reiff
- Rice University

## Radio Sounding of Plasma

- Decades of use to study ionospheric and space plasma
- Transmit a narrow pulse, listen for reflection
- Wave reflected when group refractive index goes to zero
- Sweep freq of the pulse to study plasma distribution
- Measurements are freq/time-of-flight pairs
- Alias time-of-flight to reflection distance if no refraction:
- Δxvirtual = 0.5*c*Δτ	(1)

- IMAGE Team Meeting, 22May06

## Like an echo, but from VERY far downhill

Decrease in altitude  →  increase in density of medium

Increase in density    →  refraction slows wave down

Virtual distance larger than actual distance to reflection

How to determine real distance to reflection?

- Decrease in altitude  →  increase in density of medium
- Increase in density    →  refraction slows wave down
- Virtual distance larger than actual distance to reflection
- How to determine real distance to reflection?

- Virtual distance

- IMAGE Team Meeting, 22May06

## Refraction of radio wave

- Depends on polarization
- Ordinary mode or extraordinary mode?
- Depends on frequency of wave transmitted
- Depends on gyrofrequency, plasma frequency
- Refraction is ***local*** effect
- Changes from point to point as wave travels

- IMAGE Team Meeting, 22May06

## Lamination method

- Way of solving the problem developed for ionosphere
- Huang & Reinisch, *Radio Sci.*, **17** (4), 1982 (and refs therein)
- Determine plasma resonances at sounder
- Gyrofreq, upper hybrid freq, X and O mode cutoffs
- Monotonic change in plasma density, gyrofrequency allow integrating refractive index for virtual distance
- Reinisch et al, 2001 summarizes well:

- IMAGE Team Meeting, 22May06

## Tough Problem - I

- Lamination requires starting integrating at sounder
- Uses values of plasma, gyro frequencies at source
- While RPI is transmitting, it cannot listen!
- Minimum delay time equal to width of pulse
- Therefore always a minimum virtual distance
- Local information needed for lamination not available?
- What about using local resonances?
- Bob Benson needs a clone......
- Calculated values depend heavily on B-field model if n+ 1/2 not present
- Refraction between satellite and minimum virtual distance unknown
- Want to automate using Phil Webb’s database.. (in house now...)

- IMAGE Team Meeting, 22May06

## Example: not so good

- Incomplete X-mode trace on plasmagram

- IMAGE Team Meeting, 22May06

## Tough Problem - II

- X-mode trace goes to minimum virtual dist
- Even best of plasmagrams, still have minimum virt dist...

- IMAGE Team Meeting, 22May06

## B-field dependence: the t96 model

- Cutoff freq at of min virtual dist too high

- IMAGE Team Meeting, 22May06

## B-field dependence: the t04s model

- Significantly lower cutoff at min virt dist!

- IMAGE Team Meeting, 22May06

## Are We At An Impasse?

- Goal: to investigate *global* behavior of plasma density
- Perhaps trying a different approach can be useful
- Try ***forward modeling***
- Guess what behavior might look like
- Fit for that behavior
- See if it might be reasonable technically
- See if it might be consistent with other observations
- Use the local resonances as a TEST of the model’s predictions

- IMAGE Team Meeting, 22May06

## Inversion Algorithm - I

- Use model magnetic field to get gyrofrequency profile
- Currently t96 or stormtime t04, but can use others easily
- Estimate X-mode cutoff frequency profile
- Invert definition of X-mode cutoff frequency for density
- K.G. Budden, *Propagation of Radio Waves*, 1985, ch.4
- For wave propagating in collisionless election plasma
- fX,R = 0.5*[ fCe + sqrt( fCe^2 + 4*fp^2 ) ]		(3)
- Ne ~ fp^2 = fX,R^2 - fX,R*fCe			(4)

- IMAGE Team Meeting, 22May06

## Inversion Algorithm - II

- How to estimate the cutoff frequency profile?
- Can fit gyrofreq profile reasonably well with a power law
- History of *in situ* plasma densities using power laws
- 1983: Persoon et al found nearly linear acceleration in polar cap using DE1/Alouette/ISIS1
- 1991: Chandler et al study ion outflow in the polar cap using DE1 data
- 2000: Gallagher et al presents the Global Core Plasma Model using Persoon and Chandler
- 2002a,b: Laakso et al present a large database of POLAR statistics and case studies
- 2002: Denton et al report a power law in geocentric radius for density along a field line
- 2003: Nsumei et al continues the tradition but separates out exponential Kp dependence
- 2005: Green provides a good summary in the ISSS7 conference proceedings
- 2005: Tu et al uses density profiles derived at Lowell to create “2D” pictures of density

- IMAGE Team Meeting, 22May06

## Inversion Algorithm - III

- If fCe and fp are power laws, reasonable to try one for fX,R
- RPI soundings are equal to cutoffs fX at reflection point
- Can get power law for f**X,V** for many Binbrowser traces
- But this is in virtual dist. Need power law in ***real*** dist...
- Take maximum advantage of available data:
***Use f******X,V ******as a proxy for f******p****** along the field line***

- IMAGE Team Meeting, 22May06

## Power law for fX,V - I

- First estimate:
- Basic least squares fit
-  First check:
- Least absolute deviation fit
- (much more robust to outliers)

- IMAGE Team Meeting, 22May06

## Power law for fX,V - II

- Now do smarter fit since data is ok:
- 	IDL’s conjugate gradient curve-fitting routine (based on the Numerical Recipes algorithm)

- IMAGE Team Meeting, 22May06

## Inversion Algorithm - IV

- Thus,  **f****X,R**** = 0.5*[ f****Ce**** + sqrt( f****Ce****^2 + 4* f****X,V ****^2 ) ]**      (5)
- Now do plasma freq power law
- Use coefficient and exponent from **f****X,V**** **
- Calculate constant by required that **f****X,R**** = f****X,V** at the satellite, since refraction effects insignificant at satellite
- So at IMAGE, approximation used is
- 		    **f****X,R**** = f****X,V** **= f****p****	****	****	**  		(6)
- This is reasonable for **f****p****  >> f****Ce****  **
- Happens if fCe  falls off faster than fp  and IMAGE high enough

- IMAGE Team Meeting, 22May06

## Inversion Algorithm - V

- Use profile for  **f****X,R** to redo estimate of  **f****p **
- Re-estimate the real distance cutoff frequency profile:
- f ́X,R = 0.5*[ fCe + sqrt( fCe^2 + 4* fp ^2 ) ]      	(7)
- Estimate the plasma frequency profile:
- f ́p^2 = f ́X,R^2 - f ́X,R*fCe 	 			(8)
- And now get an electron density profile:
- Ne = (f ́p/8.98)^2					(9)

- IMAGE Team Meeting, 22May06

## The algorithm in a nutshell

- First, measure f_X
- RPI sounding frequencies
- Black diamonds
- Second, fit f_X
- Solid green line
- Third, fit f_g
- Red dash-dot-dot-dot line
- Fourth, **f****X,V** → **f****X,R** → **f****p**
- Blue dash-dot line
- Fifth, **f****p** → **f ́****X,R**** **
- Burnt orange dash line
- Sixth, final density profile
- Not shown

- IMAGE Team Meeting, 22May06

## Notice behavior

- Dashed, burnt orange line is estimate for real distance cutoff frequency profile
- Acts like gyrofrequency when gyrofrequency is much larger than plasma frequency
- Switches to looking like plasma frequency profile since B-field is dropping off faster than plasma density
- Exactly what we said we needed a few slides back
- Good so far (NB: not the same plot as on previous slide)

- IMAGE Team Meeting, 22May06

## How to check?

- Traces represent guided propagation
- Fung et al, Fung and Green, Reinisch et al establish that the
- 	the traces we are using are ducted X-mode waves
- Start at satellite, integrate along field line until reflection
- Stix parameters		 →   X = f ́p^2 / f^2 ; Y = fCe / f
- phase refractive index 	 →   n^2 = 1 – X/(1-Y)
- group refractive index 	 →   n*group* = n + f * ∂n/∂f
- bookkeeping 		 →   b = X*(2 - Y) / [ω*(1 - Y)^2 ]
- n*group *= n + (0.5 * w * b / n), n*group * → 0
- do for a spectrum of test sounding frequencies
- Essentially, once we have a plasma density profile, we are doing the lamination method to investigate its quality

- IMAGE Team Meeting, 22May06

## Density power laws

- IMAGE Team Meeting, 22May06

## Validation - I

- Fixed increments between points
- Set when creating the magnetic field traces
- Add up time to propagate between consecutive points
- End up integrating c/v*group*
- This is real distance to reflection; compare against **f ́****X,R**** **
- Tests quality of code
- Still need to test against independent data (local)

- IMAGE Team Meeting, 22May06

## Validation - II

- IMAGE Team Meeting, 22May06

## Validation - III

- Plan to test against plasma densities determined from resonances at satellite
- (still in development)
- Can average exponents and compare against values from statistical studies
- Can evaluate fits at certain well-studied altitudes, average, and compare against reported values

- IMAGE Team Meeting, 22May06

## Validation - Exponents

- Exponents
- Persoon et al (geocent dist, RE) 		 →   −3.85 ± 0.32
- Gallagher et al (altitude, km)		 →   −3.09
- Laakso et al (altitude, RE)		 →   −4.4
- Nsumei et al (geocent dist, RE)	 	 →   −5.09 ± 0.03
- Our radial value, t96 (geocent dist, RE)  	 →   −7.082 ± 0.062
- Our radial value, t04s (geocent dist, RE) 	 →   −7.052 ± 0.063
- Our aligned value, t96 (geocent dist, RE) 	 →   −7.288 ± 0.064
- Our aligned value, t04s (geocent dist, RE)  →   −7.249 ± 0.064
- Appears to fall off too quickly, but actually agree in densities in locations of overlap ... our fit includes a high-altitude asymptotic density so the exponent is larger

- IMAGE Team Meeting, 22May06

## Validation - Densities

- Liu et al says 20-30,000 cm^-3 at F2 peak, ~0.047 RE altitude (European ISR remote sensing); our fits give mean densities of 32-33,000 cm^-3
- Sonwalkar et al says 800-1000 cm^-3 around ~0.623 RE altitude (IMAGE passes in the southern polar cap); our fits give mean densities of 450-400 cm^-3
- Johnson et al says 20-100 cm^-2 around 1 RE altitude (POLAR data used to investigate dependence of density upon illumination); our fits give mean densities of 90-110 cm^-3

- IMAGE Team Meeting, 22May06

## Summary/Future Work

- Over the last five years at Rice, we have created a semi-automated tool to take X-mode traces generated in Binbrowser and derive plasma density information from them, given a magnetic field.
- This tool, named rpiProfiler by Vance Henize when he started this project, has since been rigorously developed, debugged, and made more robust against the vagaries of malformed input data.
- Special care has been taken to document the code, to make it easy to maintain, and to make it easy to use.
- But can it be used to do anything other than make pretty pictures?

- IMAGE Team Meeting, 22May06

## Summary/Future Work

- The code has been run on about 1/3 of a database of X-mode Binbrowser traces selected by Vance Henize. Of the nearly 1500 not initially rejected in 2001-02, about 1100 can be successfully inverted. Further work needs to be done to quantify how reliable these inversions are.
- The power laws are a bit steep. The striking difference in traces that can be reasonably created in Binbrowser for traces corresponding to  depending on the value used for the gyrofrequency at the satellite may be a factor in the quality of the traces input to our code. It may also be that such averaging is not a useful interpretation of the density power law parameters, or that a different type of probability distribution should be used to calculate expectations for the exponents.

- IMAGE Team Meeting, 22May06

## Summary/Future Work

- The values calculated are in decent agreement with densities reported in statistical studies taken at various times at various altitude with very different instrumentation. We take this as early indication of the utility of this approach.
- Future tasks
- integrate densities from local plasma resonances, both as input and as model tests
- investigate sensitivity to trends in data not rejected computationally (lots of data is rejected so that the code doesn’t break trying to do unphysical calculations)
- all traces are from 01Aug00-31Jul01; need to begin analysis of the rest of RPI’s data set
- collaborate to compare our results with those from the other teams doing inversions

- IMAGE Team Meeting, 22May06

## Acknowledgements

- We would like to thank everyone for putting the mission together and for answering questions and fixing websites and such. Ivan Galkin answered a number of tricky questions and helped Rice rebuild its RPI level 0 archive. Nikolai Tsyganenko and Scott Boardsen gave cogent counsel regarding the use of the external field models. Andrew Urquhart provided the t96 traces to Vance Henize that became part of this project.
- This work was sponsored under the IMAGE project (may it resurrect!!)

- IMAGE Team Meeting, 22May06

## References - I

- Budden, K.G. *The Propagation of Radio Waves: The Theory of Radio Waves of Low Power in the Ionosphere and Magnetosphere*. 1985.
- Chandler, M. O., J. H. Waite Jr., and T. E. Moore, Observations of polar ion outflows, *J. Geophys. Res.*, **96**, 1421, 1991.
- Denton, R. E., J. Goldstein, and J. D. Menietti. Field line dependence of magnetospheric electron density,* Geophys. Res. Lett.*, **29 **(24), 2205, doi:10.1029/2002GL015963, 2002.
- Fung, S. F., R. F. Benson, D. L. Carpenter, J. L. Green, V. Jayanti, I. A. Galkan, and B. W. Reinisch (2003), Guided echoes in the magnetosphere: Observations by Radio Plasma Imager on IMAGE, Geophys. Res. Lett., 30(11), 1589, doi:10.1029/2002GL016531.
- Fung, S. F., and J. L. Green (2005), Modeling of field-aligned guided echoes in the plasmasphere, J. Geophys. Res., 110, A01210, doi:10.1029/2004JA010658.
- Gallagher, D. L., P. D. Craven, and R. H. Comfort, Global core plasma model, *J. Geophys. Res.*, **105**, 18, 819, 2000.
- Green, J. Magnetospheric Sounding by IMAGE, *Proceedings of ISSS-7*, 26, March 2005.

- IMAGE Team Meeting, 22May06

## References - II

- Huang, X. and B.W. Reinisch. Automatic Calculation of Electron Density Profiles from Digital Ionograms. 2. True Height Inversion of Topside Ionograms with the Profile-Fitting Method. *Radio Sci.*, **17** (4), 837, 1982.
- Johnson, M. T., J. R. Wygant, C. Cattell, F. S. Mozer, M. Temerin, and J. Scudder, Observations of the seasonal dependence of the thermal plasma density in the Southern Hemisphere auroral zone and polar cap at 1 RE, J. Geophys. Res., 106, 19,023– 19,033, 2001.
- Johnson, M. T., and J. R. Wygant, The correlation of plasma density distributions over 5000 km with solar illumination of the ionosphere: Solar cycle and zenith angle observations, Geophys. Res. Lett., 30(24), 2260, doi:10.1029/2003GL018175, 2003.
- Laakso, H., Pfaff, R., and Janhunen, P.: Polar observations of electron density distribution in the Earths magnetosphere. 1. Statistical results, *Ann. Geophysicae*, **20**, 1711, 2002a.
- Laakso, H., Pfaff, R., and Janhunen, P.: Polar observations of electron density distribution in the Earths magnetosphere. 2. Density profiles, *Ann. Geophysicae*, **20**, 1725, 2002b.
- Liu, H., K. Schlegel, and S.-Y. Ma. Combined ESR and EISCAT Observations of the Dayside Polar Cap and Auroral Oval During the May 15, 1997 Storm. , *Ann. Geophysicae*, **18**, 1067, 2000.

- IMAGE Team Meeting, 22May06

## References - III

- Nsumei, P. A., X. Huang, B. W. Reinisch, P. Song, V. M. Vasyliunas, J. L. Green, S. F. Fung, R. F. Benson, and D. L. Gallagher. Electron density distribution over the northern polar region deduced from IMAGE/radio plasma imager sounding, *J. Geophys. Res.*, **108 **(A2), 1078, doi:10.1029/2002JA009616, 2003.
- Persoon, A.M., D.A. Gurnett, and S.D. Shawhan. Polar Cap Electron Densities From DE 1 Plasma Wave Observations, *J. Geophys. Res.*, **88** (AI2), IO,I23-I0,136, 1983.
- Reinisch, B. W., X. Huang, P. Song, G. S. Sales, S. F. Fung, J. L. Green, D. L. Gallagher, and V. M. Vasyliunas, Plasma density distribution along the magnetospheric field: RPI observations from IMAGE, *Geophys. Res. Lett.*, **28**, 4521, 2001a.
- Sonwalkar, V. S., et al. (2004), Diagnostics of magnetospheric electron density and irregularities at altitudes <5000 km using whistler and Z mode echoes from radio sounding on the IMAGE satellite, J. Geophys. Res., 109, A11212, doi:10.1029/2004JA010471.
- Tu, J., P. Song, B.W. Reinisch, X. Huang, J.L. Green, H.U. Frey, and P.H. Reiff. Electron density images of the middle- and high-latitude magnetosphere in response to the solar wind. *J. Geophys. Res.*, **110**, A12210, doi:10.1029/2005JA011328, 2005.

- IMAGE Team Meeting, 22May06