bob-ipels_2005

IPELS05 – 8th International Workshop on the Interrelationship between Plasma Experiments in Laboratory and Space – July 4th-8th, 2005, Tromsø, Norway

A Laboratory Experiment of a Cyclotron Maser Instability with Applications to Space & Laboratory Plasmas

Robert Bingham, Barry J. Kellett Rutherford Appleton Laboratory Space Science and Technology Department Alan Cairns, Irena Vorgul School of Mathematics & Statistics University of St Andrews Alan Phelps, Kevin Ronald, David Speirs, A.W. Cross, C.G. Whyte and C. Robertson Department of Physics University of Strathclyde

Motivation Cyclotron Maser Radiation in Astrophysics, Space and Laboratory Plasmas

• Explain non-thermal cyclotron radio emission from stellar and planetary systems. • Devise laboratory experiments to test the models. • Laboratory experiment – “Table Top Aurora” • Develop new methods for generating microwave maser radiation in the laboratory

Cyclotron Maser Emission • Gyromagnetic Resonance

 – n – k||v|| = 0 • •

n=0 1-D Cerenkov Condition n  0   n » k||v|| Cyclotron emission or .... . absorption of O mode and X . . . mode radiation. Gyromagnetic Emission: Cyclotron: non-relativistic Gyrosynchrotron: mildly relativistic Synchrotron: ultra relativistic

Cyclotron Instabilities • Cyclotron instabilities are classified as Reactive or Kinetic • REACTIVE – Due to particle bunching – Axial bunching – along z – Azimuthally bunching – bunching in angle  associated with gyration in magnetic fields:– Example Gyrotron

• KINETIC – Maser emission results from

Parallel drive

Perpendicular drive

• First discussion of electron cyclotron maser radiation was by Twiss (1958) to describe radio astronomical sources. • Electron cyclotron maser emission is important for bright radio sources, from planets to the Sun to active flare stars.

History/Background • X-ray and radio observations of “active” stars over the past 25 years have revealed a variety of different phenomena. Probably the most significant result is the important role played by magnetic fields in these stars (and the Sun!). • However, many of the different observations appear contradictory when compared with each other. • For example, the X-ray spectral data reveals thermal emission (in the 1-30 million K range), whereas the radio data is most often believed to be non-thermal and can have brightness temperatures in excess of 1000 million K! • We started by reviewing the X-ray and radio observations of a wide range of active stars and collected together a number of observational “problems”. • We then proposed a particular magnetic configuration for these active stars and showed that with this one “assumption” we are able to explain all the observations… • … and without any of the contradictions noted above!

Observational “Photofit” • Two Temperature X-ray Plasma – 1-3 million K (i.e. very similar to the Sun!) – 10-30 million K & larger volume (much larger than the star, in fact – from eclipsing binaries) • X-ray vs Radio Luminosity • Polarized Radio Flares

• “Slingshot” Stellar Prominences • First Resolved Radio Image - UV Ceti • [X-ray Plasma Abundances]

X-ray vs Radio Luminosity of the Sun and Stars • A remarkable correlation seems to apply to the radio and X-ray emission from solar flares and active stars – covering 8-10 orders of magnitude! • But why should the X-ray and radio fluxes correlate at all?

Giant stars Dwarf stars Solar flares

Polarized Radio Flares

Stellar “sling-shot” Prominence • Slingshot prominences are seen in the optical spectra of stars as a dark “shadow” crossing the bright absorption lines of the star. • The gradient of the shadow gives information about the relative velocity of the “cloud” and hence its position or height above the star.

First Radio Image of a Star – UV Ceti

Laboratory Analog – a Toroidal Dipole Magnetic Trap • A dipole magnetic field forms a natural magnetic trap and is responsible for the radiation belts around the Earth and other planets (e.g. Jupiter). • It has been proposed as an ideal trap for fusion plasmas. • The main feature of a dipole magnetic trap is the field strength minimum at the equator and increasing in strength towards the poles. • In such a magnetic configuration charged particles will bounce back and forth between their mirror points in the northern and southern hemispheres. MAST (Culham Laboratory)

Schematic Picture of Radio and X-ray Emission • Our model for the typical active star!

Planetary Magnetospheres All solar system planets with strong magnetic fields (Jupiter, Saturn, Uranus, Neptune, and Earth) also produce intense radio emission – with frequencies close to the cyclotron frequency.

Solar wind

Planetary Aurora

Radio emission region

electron beams Animation courtesy of NASA

Jupiter’s aurora

Planetary Radio Emission

i.e. due to solar wind ram pressure

• (a) Initial radio Bode’s law for the auroral radio emissions of the five radio planets (Earth, Jupiter, Saturn, Uranus and Neptune) (Desch and Kaiser, 1984; Zarka, 1992). JD and JH correspond to the decameter and hectometer Jovian components, respectively. The dashed line has a slope of 1 with a proportionality constant of 7.10-6. Error bars correspond to the typical uncertainties in the determination of average auroral radio powers. (b) Magnetic radio Bode’s law with auroral and Io-induced emissions (see text). The dotted line has a slope of 1 with a constant of 3.10-3.

Electron acceleration in the aurora • DE-1 at 11000 km over the polar cap

Electron distribution with a crescent shaped peak in the downward direction

[Menietti & Burch, JGR, 90, 5345, 1985]

A crescent-shaped peak (p) with the addition of a field-aligned hollow (h).

Observations of auroral electrons

Mountain-like surface plot of an auroral electron distribution exhibiting a distinct beam at the edge of a relatively broad plateau.

FAST Observations of electron distributions in the AKR source region • Delory et al. - GRL 25 (12), 2069-2072, 1998. Delory et al. reported on high time-resolution 3-D observations of electron distributions recorded when FAST was actually within the AKR source region. In general, the electron distributions show a broad plateau over a wide range of pitch angles. They presented computer simulations of the evolution of the electron distribution which assumed plasma conditions similar to those observed by FAST and which show similar results to those observed.

FAST Observations - Delory et al. GRL, 25(12), 2069, 1998 •

The observed radio emission from UV Ceti is actually remarkably similar in form to the Earth’s AKR emission [AKR = Auroral Kilometric Radiation]. Here are some measurements of the electron distribution functions seen in the AKR formation region.

Strangeway et al. 2001 – FAST Data “Cartoon” The figure shows an electron distribution function acquired by FAST within the aurural density cavity (see later). This is the region where the auroral kilometric radiation (AKR) is generated. The figure also shows the envisaged flow of energy. Parallel energy gained from the electric field (stage 1) is converted to perpendicular energy by the mirror force (stage 2). This energy is then available for the generation of AKR and diffusion to lower perpendicular energy (stage 3).

Auroral Kilometric Radiation • Emission from low density channels in auroral region.

• Narrow bandwidth at frequency just below electron cyclotron frequency. • Polarised in X mode and generated near perpendicular to magnetic field. Explanations have tended to focus on loss-cone instability, but we suggest cyclotron instability associated with formation of “horseshoe” distribution in beams.

Bandwidth and Polarization • The bandwidth is also extremely narrow, from the figure estimated to be about 0.05% or around 200 Hz. • Also in agreement with observations is the polarization in the R-X mode. SATURATION Non-linear saturation by decreasing μ0 i.e. the opening angle and thermally spreading the beam.

Horseshoe Formation Field aligned electron beams naturally form a horseshoe distribution as they move into stronger magnetic field regions. The adiabatic invariance v2 /B = constant causes the electrons to lose parallel energy and increase their perpendicular energy producing the characteristic horseshoe distribution with fe / v > 0.

Requirements

f e 0 v  where

 c   pe

eB c  , me

ne   pe   0   me 0  2

Low density cold background such that nH > nC

1

2

 AURORAL KILOMETRIC RADIATION

DOWNWARD ACCELERATED ELECTRONS

AURORAL

DENSITY CAVITY

Evolution of an auroral electron energy beam distribution (Bryant and Perry, JGR, 100, 23711, 1995) A-H show different altitudes evenly space between 24000 and 1000 km. The velocity range is from 0 up to 80 km/s. Acceleration was assumed to take place for 2000 km immediately below A. This acceleration produces a fieldaligned beam at B which steadily widens to become the crescent-shaped feature in G and then widens even further to become almost isotropic in H. A crucial feature of the wave theory is the symmetry outside the loss cone about the zero parallel velocity axis, revealing that the conic is simply the magnetically mirrored outer part of the down-going beam.

Formation of horseshoe distribution. 2

2

2

2

1.5

Beam with thermal spread moving down converging magnetic field lines. Conservation of A0 magnetic moment means A0 that particles lose parallel energy and gain perpendicular energy. Here, we show the evolution of beam with initial Maxwellian spread, moving into increasing B field.

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Cyclotron resonance condition:



nce



 k||v||  0

For small parallel wavenumber, resonant frequency is shifted below cyclotron frequency by an amount dependent on the particle energy. The effect of cyclotron resonance is to produce diffusion of the particle in velocity space, mainly in the perpendicular degree of freedom ( entirely in the perpendicular direction for propagation normal to the field). This follows from momentum conservation.

Theory Dielectric tensor element (from Stix)

 2pe  xx   ce 2



  2 p n

2

0

  dp

 ce /

 dp   k v  n ||



|| ||

n J n (z) f 0 k || f 0 f 0  p[  (v  v|| )] 2 p  p|| p z with

z

k v

 ce

ce

/

Some Assumptions Make following simplifications:• Put k|| = 0. • Use cold plasma approximation for real part. • Take account of imaginary part from n =1 term, assuming radiation near fundamental cyclotron frequency. • Assume z small, (effectively saying that perpendicular velocity spread 1km) wound on non-magnetic formers, tubing is core cooled by water at 20Bar • Drive up to 6 Solenoids independently up to 600A with 120kW DC power supplies • Allows flexible control of the magnetic field configuration and therefore of the rate and degree of magnetic compression

Solenoid Configuration Axial magnetic field profile of AKR experiment (Bz /Bz0 = 34)

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0.5 Experimental magnetic field profile End of solenoid 1 (diode coil) Position of cathode

Bz (Tesla)

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z (m)

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During Construction … Solenoid 1: 4 Layers, Length = 0.25m, Ri = 0.105m, Current = 75A. Solenoid 2: 2 Layers, Length = 0.5m, Ri = 0.105m, Current = 60A. Solenoid 3: 10 Layers, Length = 0.5m, Ri = 0.05m, Current = 250A.

Solenoid 4: 2 Layers, Length = 0.11m, Ri = 0.12m, Current = 250A. Solenoid 5: 2 Layers, Length = 0.11m, Ri = 0.12m, Current = 250A.

Solenoids 1 and 2 complete and mounted on the solenoid winding rig. A shared UPVC former was used with the excess visible next to the end capstan.

Experimental Progress • Coil fabrication complete, experimental chamber evacuated to 10-9 Bar • Water cooling pump/distributors and drive power supplies installed • Major apparatus assembly completed • Experiments now underway

Apparatus

Electron Gun and Faraday Cup

Microwave output frequency Rectifying crystal output vs cutoff filter specification 0.04 0.02

Signal amplitude (Volts)

0 0

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200

-0.02 -0.04

No filter 11.5GHz cutoff filter 12.7GHz cutoff filter

-0.06 -0.08 -0.1 -0.12 -0.14 Time (ns)

Microwave output frequency

NB: Note observed frequency ~11.6-11.7 GHz!

Microwave Antenna Pattern Azimuthal mode profile for a diode solenoid current of 40A 1.8

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Relative amplitude

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1 First peak Second peak 0.8

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Angle (degrees)

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Mirroring of Electron Beam Ibeam/Idiode vs Mirror Ratio Bz / Bz0

Ibeam / Idiode

0.5 0.45

Diode coil current = 40A Diode coil current = 90A

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Diode coil current = 150A

0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0

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Mirror Ratio (Bz / Bz0)

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Summary • An experiment has been devised to investigate a proposed new mechanism for Auroral Kilometric Emission • The apparatus has been developed in conjunction with PiC code simulations of the geometry and field configurations to allow the formation of an electron beam having a horseshoe distribution in phase space via a highly configurable process of magnetic compression • Major component fabrication is now complete • Experiments to test the validity of the mechanism are underway with the results being compared against recent developments of the theory (at St. Andrews University) to account for a metallic bounded geometry

Conclusions  The cyclotron maser instability generated by the horseshoe distributions observed in the auroral zone can easily account for the AKR emission, stellar radio emission, pulsars?.  Laboratory AKR Experiment – “table-top aurora”  Confirms horseshoe generation mechanism  Bandwidth and mode conversion agree with theory  We have direct access to a “laboratory” for studying the radio emission from planetary and stellar sources!

Future Work • Accurate characterisation of the emitted radiation (frequency, power modal content)

• Investigate growth rate of the instability by reconfiguring the apparatus to act as an amplifier • Compare measurements of growth rate with theory • Understand if the instability may have practical implementations Acknowledgements This work was funded by the EPSRC (new extension grant applied for!)