Incoherent Scatter theory and its application at the magnetic Equator Marco A. Milla Radio Observatorio de Jicamarca Instituto Geofísico del Perú JIREP Seminar, June 3, 2013
Jicamarca Radio Observatory
Jicamarca Radio Observatory Our main instrument is one of the largest incoherent scatter radars in the World. It is a research center to study the ionosphere and upper atmosphere. Located at ~20 km east of Lima, Peru. (11.95 S, 76.87 W). It is part of a chain of observatories extending from Greenland to Peru. Operates a variety of instruments: IS an CS radars, ionosondes, magnetometers, GPS receivers, Fabry Perot interferometers.
Characteristics of the Jicamarca Radar Operating frequency: 50 MHz Antenna: array of 18,432 halfwave dipoles covering an area of 300 x 300 m 2. The antenna is composed of 8x8 cross-polarized modules. Pointing directions: within 3 degrees from on-axis. Phase changes are done manually. Transmitters: 3 x 1.5 MW peakpower with 5% duty cycle. Fourth TX under construction.
Why at Jicamarca? It is under de magnetic Equator (use of large horizontal antenna). It was built between 1960-1962. Dr. Ken Bowles, the founder of Jicamarca, worked in Peru (with IGP people) during the IGY 1958. It is free of electromagnetic interference (surrounded by mountains).
What do we study at Jicamarca?
What do we study at Jicamarca? ISR
What do we study at Jicamarca? ISR Density, temperature, composition, electric fields Modeling, space weather
What do we study at Jicamarca? Coherent Scatter Radar ISR Density, temperature, composition, electric fields Modeling, space weather
What do we study at Jicamarca? Neutral atmosphere dynamics (winds, turbulence, vertical velocities) Meteorology, aviation. Coherent Scatter Radar ISR Density, temperature, composition, electric fields Modeling, space weather
What do we study at Jicamarca? Ionospheric Irregularities (EEJ, 150-km, ESF). SAR, GPS Neutral atmosphere dynamics (winds, turbulence, vertical velocities) Meteorology, aviation. Coherent Scatter Radar ISR Density, temperature, composition, electric fields Modeling, space weather
What do we study at Jicamarca? Ionospheric Irregularities (EEJ, 150-km, ESF). SAR, GPS Neutral atmosphere dynamics (winds, turbulence, vertical velocities) Meteorology, aviation. Neutral turbulence MST Coherent Scatter Radar ISR Density, temperature, composition, electric fields Modeling, space weather ESF: Spread F 150-km echoes EEJ: Equatorial Electrojet PEME
What do we study at Jicamarca? Ionospheric Irregularities (EEJ, 150-km, ESF). SAR, GPS Neutral atmosphere dynamics (winds, turbulence, vertical velocities) Meteorology, aviation. Neutral turbulence MST Coherent Scatter Radar ISR Meteors Density, temperature, composition, electric fields Modeling, space weather ESF: Spread F 150-km echoes EEJ: Equatorial Electrojet PEME
More about what we study at Jicamarca Dynamics of the equatorial ionosphere - Physical parameters (Ne, Te, Ti, Vd, Zd, %O +, %H +, %He + ). - Spectral characteristics of plasma irregularities (Electrojet, Spread- F, 150km echoes). Dynamics of the neutral atmosphere - MST (Mesosphere, Stratosphere, and Troposphere). Meteor detection and characterization. Radio astronomy, others. Ne Vd Spread-F
A typical day above Jicamarca ExB drifts from 150- km first moment. Plasma physics from EEJ spectra. Plasma physics and lower thermosphere winds from nonspecular meteor trails. Mesospheric winds from mesospheric echoes.
A typical night above Jicamarca Effect of the F-region dynamics near sunset on the generation of Spread-F plumes.
Incoherent scatter theory Standard model
Incoherent Scatter Radars (ISR) They are big systems with large high-gain antennas. Their transmitters deliver power in the order of megawatts. Their targets are the electrons moving in the Ionosphere. The signal scattered by the electrons is in picowatts, thus the need of sensitive receivers. The spectrum of the returned signal provides information about the density, temperature, composition and drift velocity of the Ionospheric plasma as function of height.
Thomson scattering from free electrons Volume V Each free electron in the ionosphere radiates back a weak Thomson scattered field with a Doppler shifted frequency and some known average power P e P t σ e where σ e 10 28 m 2 is the backscatter RCS of a free electron.
Thomson scattering from free electrons Volume Density V N Each free electron in the ionosphere radiates back a weak Thomson scattered field with a Doppler shifted frequency and some known average power P e P t σ e where σ e 10 28 m 2 is the backscatter RCS of a free electron. Assuming independent phases, the average scattered power from ionospheric electrons adds up incoherently, and the scattered signal spectrum resembles the radial velocity distribution of the electrons --- a Gaussian with a frequency width 2k o C e and a total average power P e VN
IS Theory - Thomson Scattering 1 Each electron reradiate an electric field proportional to r e r E ie j k B r p Contributions from all electrons in ΔV are collected by the radar antenna such that r p v p v a (t) N V p=1 e j k B r p (t) Free electrons k Computing the ACF of this voltage, we have v a (t + )v a(t) N V N V e j k B ( r p (t+ ) r p (t)) p=1 p =1
IS Theory - Thomson Scattering 2 Assumptions: 1. Trajectories are independent. v a (t + )v a(t) 2. Electrons move in straight line trajectories. ( r p (t) = v p t ) v a (t + )v a(t) N 3. Velocities have a Maxwellian distribution pdf( v p ) = exp( v p v p 2C ) e 2 ( C e = KT e 2 C e ) 3 m e V p=1 N e j k B ( r p (t+ ) V p=1 e j k B ( v p ) r p (t)) Free electrons r p v p k
IS Theory - Thomson Scattering 3 We finally obtain that v a (t + )v a(t) N V e 1 2 k2 B C2 e Some definitions: 1. Density fluctuation function 2. Single particle correlation where n( k, t) = N e j k B r p ( ) = r p (t + ) r p (t) V p=1 is the displacement. e jk r p(t) r p ( ) 2 ACF Power Spectrum 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ACF Electron (Te = 1000K) 0 0 5 10 15 20 Time (µsec) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 1 x 105 Thomson Spectrum Te = 1000K d e j 0 100 50 0 50 100 Frequency (khz) e 2 2k 2 B C2 e
Bowles (1958) carried first successful experiment at Long Branch, Illinois. Operating frequency: 40.92 MHz Peak pulse power: 4 to 6 MW Antenna area: 116 x 140 m 2 Electrons do not control the spectrum. The ions dominate. Fejer (1960), Dougherty and Farley (1960,1963), Salpeter(1960), Hagfors (1961), Rosenbluth and Rostoker(1962), Farley (1966), Woodman (1967) developed the theory. First ISR Observation
... but individual electrons in the ionosphere do not exactly behave as independent radar targets, and, as a consequence, Not true Nk,Ω 2 Signal spectrum 1 0.8 0.6 0.4 0.2-3 -2-1 1 2 3 Ω k C e Power P = P e NV Incoherent scatter but not observed
... but individual electrons in the ionosphere do not exactly behave as independent radar targets, and, as a consequence, Not true... instead Signal spectrum Nk,Ω 2 1 0.8 0.6 Nk,Ω 2 0.0004 0.0003 0.4 0.0002 0.2 0.0001-3 -2-1 1 2 3 Ω k C e -3-2 -1 1 2 3 Ω k C i Power P = P e NV P = P env 2 for T e = T i Incoherent scatter but not observed
... but individual electrons in the ionosphere do not exactly behave as independent radar targets, and, as a consequence, Not true... instead Signal spectrum Nk,Ω 2 1 0.8 0.6 Nk,Ω 2 0.0004 0.0003 0.4 0.0002 0.2 0.0001 Power -3-2 -1 1 2 3 P = P e NV Incoherent scatter but not observed Ω k C e -3-2 -1 1 2 3 Ω k C i P = P env for T e = T i 2 The frequency spectrum (PSD) of a thermally excited plasma density waves with a wavenumber k =2k o.
IS Theory - Collective interactions However, electrons and ions do interact between each other. n( N V N V k, ) 2 1 = d e j e j k ( r p (t+ ) V p=1 p =1 = N d e j e j k r e ( ) = n te ( (k), ) 2 How to deal with the correlation between trajectories? Split the density fluctuations in collective and non-collective n e = n te + n e e = n te e k E Similarly for the ions we have: r p (t)) Electrons + ions n i = n ti + i e k E k
IS Theory - Calculating ISR spectrum Poisson Equation: j o k E = e(ni n e ) Combining these three equations and assuming that the thermal fluctuations are random independent variables, we obtain ω k e n i E ω k e n j ω o σ i σ e ω k e n ti ω k e n te n ( k, ω) 2 = j ω o + σ i 2 n te ( k, ω) 2 j ω o + σ e + σ i 2 + σ e 2 n ti ( k, ω) 2 j ω o + σ e + σ i 2 The IS theory provides an expression for the spectrum of density fluctuations in terms of the conductivity and thermal fluctuations of each specie in a plasma.
IS Theory - Standard Model The thermal density fluctuations and conductivity in thermal equilibrium are related to each other by the Nyquist theorem. n ts ( k, ω) 2 N o = 2Re{ J s ( ω s ) } σ s ( k, ω) j ω o = 1 j ω s J s ( ω s ) k 2 h 2 s In addition, both can be calculated in terms of the Gordeyev integral that can be interpreted as the one sided Fourier Transform of the ACF of the scattered signal by a single particle.
True ISR Spectrum 1 x 105 Thomson Spectrum Te = 1000K 5 x 104 IS Spectrum Te = 1000K, Ti = 1000K 0.9 4.5 0.8 4 0.7 3.5 Power Spectrum 0.6 0.5 0.4 Power Spectrum 3 2.5 2 0.3 0.2 0.1 1.5 1 0.5 Spectral width of the order of the ion thermal speed 0 100 50 0 50 100 Frequency (khz) 0 2 1.5 1 0.5 0 0.5 1 1.5 2 Frequency (khz)
Incoherent scatter theory Magnetic field effects
IS radars in the world
IS radars in the world
IS radars in the world
IS radars in the world
IS radars in the Magnetic equator Jicamarca
IS radars in the Magnetic equator Altair Jicamarca
Jicamarca radar - Spectral Data 800 Channel 1 20040608 11:55:00 30 700 600 25 Incoherent scatter spectrum narrows at perpendicular to B. Range (km) 500 400 20 db 27 26 Channel 1 20040608 11:55:00 280.00 km 300.00 km 320.00 km 340.00 km 300 200 150 100 50 0 50 100 150 Doppler velocity (m/s) The data is used to measure the plasma drifts (doppler shift). 15 Power Spectrum (db) 25 24 23 22 21 150 100 50 0 50 100 150 Doppler velocity (m/s)
IS Theory - DC Magnetic Field 1 Charged particles move in helical trajectories parallel to B tie to a fixed magnetic field line. The single particle ACF is given by e j k r s = e 1 2 k2 r2 s e 1 2 k2 p 2 s where r 2 s = C 2 s 2 p 2 s = 4C2 s 2 s sin 2 ( s 2 ) Electrons B ACF 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ACF Electron (Te = 4000K) Highly oscillatory 0 0 5 10 15 20 25 30 35 Time (Number of periods) ACF 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 ACF Ion (Ti = 1000K) Less frequent oscillations 0 0 0.5 1 1.5 2 2.5 3 3.5 Time (Number of periods) Gyro-frequency k s = q sb m s
IS Theory - DC Magnetic Field 2 At perpendicular to B, the projection of the trajectory on the direction of the propagation vector is periodic. e j k r s = e 1 2 k2 r2 s e 1 2 k2 p 2 s 1 0.9 ACF Te = 4000K Ti = 1000K B 0.8 0.7 0.6 Electrons k ACF 0.5 0.4 0.3 0.2 0.1 Electron Ion 0 0 0.5 1 1.5 2 2.5 3 3.5 Time (Number of periods) Thus, theoretical ISR spectrum becomes singular at perpendicular to B (α=0).
... but experimental measurements show that the spectrum is not singular. 27 26 Channel 1 20040608 11:55:00 280.00 km 300.00 km 320.00 km 340.00 km Power Spectrum (db) 25 24 23 Collisions are responsible for the loss of correlation across the magnetic field. 22 21 150 100 50 0 50 100 150 Doppler velocity (m/s)
Coulomb Collisions In a partially ionized plasma, trajectories of charged particles colliding against neutral atoms exhibit "straight-line" motion. However, in fully ionized plasmas, the Coulomb force will deflect the charge particles before they effectively collide. In this case, the trajectory of a "test" charged particle exhibits continuous small-angle deflections of its direction of motion. Trajectory of a neutral particle in a partially ionized gas. Trajectory of a "test" charged particle (electron) in a fully ionized. _ F = 1 4πɛ 0 q 1 q 2 r 2
Trajectories in a magnetized plasma Electron trajectory under collisions An electron or ion under the presence of a DC magnetic field will move in a helical trajectory. But the deflections caused by collisions will make the charged particle not to be tied to the same magnetic field line. How can we model the effect of collisions? Well, we can represent their effects by considering some frictional and diffusive forces. zaxis 0 0.5 1 1.5 2 0.15 0.1 0.05 yaxis 0 0.05 0.05 Note: The particle will suffer friction and diffusion that may be different for the directions parallel and perpendicular with respect to the magnetic field. 0 0.05 xaxis 0.1 0.15
Oxygen Gyro-resonance The non-collisional theory predicted that at small aspect angles (<3 deg), the ISR spectrum should be highly oscillatory, with a peak-to-peak separation approximated equal to the ion gyro-frequency. Power Spectrum 6 x 104 5 4 3 2 O+ Gyroresonance Te = Ti = 1000K = 2 No collisions With collisions 1 ACF Ion (Ti = 1000K) 1 ACF 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.5 1 1.5 2 2.5 3 3.5 Time (Number of periods) 0 0 200 400 600 800 1000 Frequency (Hz) However, collisions destroy the periodicity of the O+ single particle ACF, therefore, no O+ gyro-resonance was/is observed.
IS Theory at perpendicular to B 1967: Woodman developed a IS theory that takes into account Coulomb collision effects but using a simplified Fokker-Planck collision model. 1999: Kudeki et al. estimated the vertical drift from the doppler shift of the ISR spectrum, but did not succeed in estimating the temperature from the width of the spectrum. 1999: Sulzer & Gonzalez proposed that the Coulomb collisions between electron and ions influence the shape of the spectrum at perpendicular to B. This work is based on a Monte Carlo simulation of the trajectory of an electron in the plasma. (Only for Jicamarca - 50 MHz) 2004: Woodman proposed a simplified collision model with a collision frequency that depends on magnetic aspect angle, based on the work developed by Sulzer. (Only for Jicamarca - 50 MHz)
... but experimental measurements show that the spectrum is not singular. Power Spectrum (db) 27 26 25 24 23 22 Channel 1 20040608 11:55:00 280.00 km 300.00 km 320.00 km 340.00 km S&G (1999) model, although accurate for angles between 0.5 and 3 deg, has the same problem, the spectrum becomes singular at perpendicular to B. 21 150 100 50 0 50 100 150 Doppler velocity (m/s)
more on Coulomb collisions in a few weeks...
Modes of radar operation at Jicamarca
Incoherent scatter modes Modes Range (km) V z V x N e T e T i + Faraday / Double Pulse 200-800 1 Vertical Drift 200-930 2 East-West Drift 200-930 Alternating Code (AC) 450-1400 2 Long Pulse 600-3000 2 Hybrid AC-Faraday 200-1400 3 Differential Phase (or DVD) 90-930 3,4 3 3 3 1 from 150-km echoes, only daytime. 2 Relative values 3 In progress 4 From EEJ echoes for the lower heights
Ionospheric physical parameters Ne Te Ne profiles can be obtained from calibrated power measurements. Te and Ti are obtained from fits of measured ISR ACFs. Ti Vd Vertical & Zonal drifts are estimated from the Doppler shift of ISR spectra. Zd
Summary The incoherent scatter radar technique is the most powerful technique to probe the Earth s ionosphere. Using IS radars, we can measure densities, temperatures, drifts, and composition of the ionospheric plasma as function of height. When pointing perpendicular to B, Coulomb collisions between plasma particles have an effect in the shape of the measured incoherent scatter spectrum, so the theory needs to include those effects. When pointing away from perpendicular to B, collisions are not important and therefore their effects can be neglected.