Laboratory simulation of magnetospheric chorus wave generation

Transcription

1 Plasma Phys. Control. Fusion 9 (17) 1416 (1pp) Plasma Physics and Controlled Fusion doi:1.188/ /9/1/1416 Laboratory simulation of magnetospheric chorus wave generation B Van Compernolle 1, X An, J Bortnik, R M Thorne, P Pribyl 1 and W Gekelman 1 1 Department of Physics, University of California, Los Angeles, CA, USA Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA, USA bvcomper@physics.ucla.edu Received 1 July 16, revised 9 August 16 Accepted for publication September 16 Published 18 October 16 Abstract Whistler mode chorus emissions with a characteristic frequency chirp are important magnetospheric waves, responsible for the acceleration of outer radiation belt electrons to relativistic energies and also for the scattering loss of these electrons into the atmosphere. A laboratory experiment (Van Compernolle et al 1 Phys. Rev. Lett , An et al 16 Geophys. Res. Lett.) in the large plasma device at UCLA was designed to closely mimic the scaled plasma parameters observed in the inner magnetosphere, and shed light on the excitation of discrete frequency whistler waves. It was observed that a rich variety of whistler wave emissions is excited by a gyrating electron beam. The properties of the whistler emissions depend strongly on plasma density, beam density and magnetic field profiles. Keywords: whistler, magnetosphere, chorus, laboratory (Some figures may appear in colour only in the online journal) 1. Introduction Whistler-mode chorus emissions are naturally-occurring electromagnetic plasma waves found predominantly in the low-density region outside the plasmasphere. The global distribution is such that chorus waves tend to be strongly confined to equatorial regions on the nightside, propagate to higher latitudes on the dawn side, and propagate to very high latitudes on the dayside of the Earth, possibly even impinging on the plasmasphere and evolving into plasmaspheric hiss in the process [3 8]. These waves play a key role in various magnetospheric processes, and rank as one of the most intense emissions in the inner magnetosphere, with intensities of large amplitude chorus sometimes reaching to 1 nt or more [9 13]. Characteristically, chorus is observed as a series of short (.1 s) chirps, occurring in two distinct frequency bands that peak in power near.34 fce (lower band) and.3 fce (upper band), where fce is the equatorial gyrofrequency along that field-line [14, 1], and exhibiting a wave power minimum near. fce [16, 17]. Perhaps the most distinctive feature of the chorus emission, is its discrete, narrowband structure in the frequency-time domain, exhibiting frequency tones that can rise at a rate of. khz s 1, but can also sometimes /17/1416+1$33. fall, or have a mixed rising and falling behavior. In a graphical frequency-time representation, these tones can appear as curved lines, hooks or inverted vees [14, 1, 18]. There often is an additional periodicity imposed on the sequence of chorus elements, having a timescale of a few tens of seconds, which was recently found to be well-correlated with (and hence the driver of) the pulsating aurora [19, ], as well as the diffuse aurora [1]. It is well-known that chorus intensity and occurrence are directly related to geomagnetic activity [3, 6 8, 1, 16, 7] and it is generally agreed that the generation mechanism involves cyclotron resonance with eastward drifting, freshlyinjected, unstable electron populations in the 1 1 kev range, though the exact generation mechanism remains a topic of intense research [18, 8 36]. Extensive theoretical work has been done in the past but none adequately describes the complex features of discrete, chirping chorus waves. For instance, linear theory [37] predicts the regions in the frequency domain that are unstable to wave growth, but cannot predict the saturation amplitude of the wave, nor the discreteness or frequency chirp rate. Extensive numerical simulations have been performed [3, 36, 38] under fairly restrictive assumptions that reproduce some of the features of chirping chorus waves, and 1 17 IOP Publishing Ltd Printed in the UK

2 Plasma Phys. Control. Fusion 9 (17) 1416 certain scaling laws have been developed as a result, but these laws require extensive testing against observations to ascertain their validity. Such experimental testing is difficult to perform in space, since spacecraft do not generally have access to the source distribution of electrons that originally generated the waves. In spite of the general lack of understanding of the physical processes that create the observed characteristics of chorus waves, it is well known that chorus waves play a key role in various magnetospheric processes. Recent observations made by NASA s Van Allen Probes and THEMIS missions for example have demonstrated that chorus waves play a critical role in creating the relativistic and ultra-relativistic radiation belts that encompass the Earth, that are a known hazard to astronauts and spacecraft technology failures [39 41]. Chorus waves locally transfer a portion of their energy to higher energy seed electrons (>1 kev), that are further accelerated to relativistic energies ( MeV) [4, 43]. Chorus waves also play an important role in phenomena that impact ionospheric conductivity such as the diffuse and discrete auroral emissions. In the experiment presented here, in order to study the excitation of whistler waves in a laboratory plasma, an electron beam with finite pitch angle is used as the free energy source. Whistler-mode emissions by beam-plasma interaction have been studied extensively in the past, such as in the generation of auroral hiss [44 46], in active experiments in the space environment [47 ] and in controlled laboratory settings [1,, 1 4].. Laboratory simulations Even though space plasmas are a readily available natural environment for studying plasma phenomena, a number of challenges, such as limited in situ measurements and lack of control over plasma parameters, make it difficult to tackle the chorus wave generation problem. Laboratory simulations can shed new light on the excitation mechanisms of whistler waves, and have the advantage of active control over the free energy source and over the plasma parameters, as well as the advantage of in situ diagnostic capabilities, which is needed for a first-principles, physics-based understanding. Space physics observations and current theoretical models give guidance on the essential ingredients for a laboratory simulation, and which parameters are likely to play a defining role. Li et al [] showed that whistler-mode emissions in the typical chorus region, tended to have a broadband structure for a surprisingly large portion of the observation time, associated with larger (>6 or so) values of ω pe / Ω e, whereas narrowband rising and falling tones are only observed for a range < ωpe/ Ω e < 6. A follow-up study [6] showed that both rising and falling tones were associated with fairly modest, limited ranges of the normalized beam density nb/ n (labeled nh/ nt in their paper) whereas broadband emissions had larger values. More recently [7], it was shown that chorus emissions tend to be momentarily excited on the dayside, very close to the inner edge of the magnetopause when interplanetary shocks Table 1. Plasma parameters in the laboratory and in the magnetosphere, plasma density [9]; magnetic field strength; ratio of plasma frequency to cyclotron frequency [6]; ratio of beam density to plasma density [6]; ratio of whistler wave amplitude to background magnetic field strength [6, 6]; ratio of energetic electron velocity to speed of light; ratio of electron thermal pressure to magnetic pressure. LAPD compressed the dayside magnetopause and flattened out (i.e. decreased the inhomogeneity) of the background magnetic field. Theoretical models, such as the Omura model [3, 8] hinge on the existence of a gradient in the magnetic field, and predict an optimum wave amplitude for the amplification of chorus waves. This leads to the following requirements for the experiment to be successful: (1) The need for a free energy source for the excitation of whistler waves which consists of energetic electrons with finite pitch angle; () The need to control the ratio of ω pe / Ω e ; (3) The need to control the ratio of beam density to background density nb/ n, which will also affect the ratio of the wave amplitude to the background field Bw/ B; and (4) The need to establish and control a gradient in the background magnetic field. In order for the experimental results to directly relate to magnetospheric physics it is important to obtain similar scaled plasma parameters. The whistler dispersion relation for a cold plasma is given by kc ω = ωpe, (1) ω Ω e( cos( θ) ω/ Ω e) where c is the speed of light, k is the wave number, ω is the wave frequency, ω pe is the electron plasma frequency, Ω e is the electron cyclotron frequency, and θ is the angle between the wave vector and the magnetic field direction. Typical plasma parameters in the magnetosphere have the plasma density n in the range of cm 3 and a magnetic field strength B in the range of milli Gauss. Wave frequencies are in the khz range and wavelengths in the kilometer range. Typical laboratory parameters have n cm 3, B 1 1 G, 9 with whistler frequencies in the MHz to GHz range and wavelengths which are centimeter scale. It is obvious that the physical parameters in space and the laboratory are vastly different. What matters however for the physics are scaled dimensionless parameters. Equation (1) can be rewritten as κ ωpe/ Ωe =, () ω ω ( cos( θ) ω ) with κ = kc/ Ω e, ω = ω/ Ω e. It is clear that the ratio ω pe / Ω e is the controlling factor in the whistler dispersion relation, and Inner magnetosphere n (cm 3 ) B (G) ωpe/ Ωe nb/ n B / B v/c β e

3 Plasma Phys. Control. Fusion 9 (17) 1416 Figure 1. (a) Schematic of the experimental setup, not to scale. A 1 cm diameter electron beam launches electrons with energies up to 4 kev. Probes measure plasma parameters and detect wave activity. (b) Picture of probe used to measure magnetic and electric field fluctuations. the values for ω pe / Ω e in the laboratory should be similar to those in the magnetosphere in order for the laboratory simulation to be relevant. Other important dimensionless parameters have to do with the coupling of energetic electrons to whistler waves. It is generally thought that whistler waves are excited through cyclotron resonance, i.e. ω kv = n Ω e, where v is the parallel velocity of the energetic electrons, and n =..., 1,, 1,... (n = 1 for cyclotron resonance). The scaled resonance condition equation is then v ω κ = n (3) c identifies the factor v / c as a determining factor. A further parameter of consequence to non-linear whistler wave physics is the electron trapping rate, which will determine the onset of non-linear effects. The relevant trapping rate is given by ν Te = ekbwv / me, with B w the amplitude of the whistler wave magnetic field fluctuations. The scaled form of the trapping rate, normalized to the electron cyclotron frequency, is written as νte κ Ω = Bw v B c, (4) e which denotes the importance of the strength of the whistler wave through the ratio of the whistler wave amplitude to the background magnetic field strength Bw/ B. Table 1 summarizes the parameters in the magnetosphere and in the laboratory (for the present study), both in absolute numbers and as scaled quantities. 3. Experimental setup The experiment is performed on the upgraded large plasma device (LAPD) [61, 6] at the basic plasma science facility (BaPSF) at UCLA. A schematic, not to scale, is shown in figure 1. The LAPD is a cylindrical device, with axial magnetic field that confines a quiescent plasma column 18 m long and 6 cm in diameter. The plasma is created from collisional ionization of He gas by 7 ev electrons from a large area lowvoltage electron beam, produced by the application of a positive voltage between a barium oxide (BaO) coated cathode and a mesh anode cm away. The electron beam heats the plasma to electron temperatures in the range of ev. The active phase lasts for 1 ms and is repeated every second (1 Hz pulse rate). The whistler wave experiment is performed in the afterglow phase, after the active phase of the LAPD discharge. In the afterglow phase, the 7 ev beam is turned off, and the electron temperature falls below. ev within a few 1 μs and then remains constant. The density decreases exponentially with a time constant of tens of milliseconds while the whistler wave experiment lasts 1 μs. Thus, the density of the background plasma is essentially fixed during the whistler wave experiment. The background density at which the experiment is performed can therefore be chosen by varying the time at which the experiment starts in the afterglow phase. The time evolution of the electron density in the afterglow phase is shown in figure, with the typical length of the whistler wave experiment indicated by the two vertical dashed lines. The LAPD is readily diagnosable with 4 ports and probe access every 3 cm along the machine. Probes are 3

4 Plasma Phys. Control. Fusion 9 (17) 1416 Figure. Evolution of the electron density during the afterglow phase. The active phase of the LAPD ends at 1 ms. The typical length of the whistler wave experiment is 1 μs, indicated by the two vertical dashed lines. inserted in the machine through ball valves [63] which allow for 3D movement. Probes are mounted on an external probe drive system and can be moved to any (x, y) position with sub-millimeter accuracy. The data acquisition system is fully automated and programmable, and controls the digitizers and the probe drive system. Typically, the probe moves through a series of user defined (x, y) positions at fixed z. At each position, data from several plasma shots is acquired and stored, before moving to the next position on the (x, y) grid. Since the LAPD plasma is highly reproducible, an ensemble measurement of the plasma parameters can thus be obtained in a D plane at fixed z location. The plasma is diagnosed with Langmuir probes, magnetic field and electric field probes, and retarding field energetic particle detectors. Langmuir probes are mainly used to measure the background electron density and temperature. Density measurements are calibrated with microwave interferometers which measure the line-integrated density across the column. Whistler wave fluctuations are detected with the probe displayed in figure 1(b). It consists of three orthogonal coils. Each coil has a diameter of mm and consists of a single balanced loop. The magnetic field probe and the amplifying circuitry was tested to have a flat response in the frequency range of MHz 1 GHz. For our experimental parameters the lower frequency limit corresponds roughly to the lower hybrid frequency, while the upper frequency limit is several times the electron cyclotron frequency. The probe also has three orthogonal dipoles used for electric field measurements. In this paper only magnetic field data will be presented. A 1 cm diameter electron beam source is introduced into the machine (figure 1) facing the LAPD plasma source. The electron beam source is based on a lanthanum hexaboride cathode (LaB 6 ) developed earlier at LAPD [64]. LaB 6 is a refractory ceramic material and is stable in vacuum. It has a low work function, around. ev, and one of the highest electron emissivities known when heated to its operating temper ature in the range of 18 K. Figure 3 shows the inner structure of the electron beam source. A snaked carbon heating element sits close to a ceramic disk supporting a 1 cm LaB 6 disk. A DC current resistively heats the carbon heating element Figure 3. Inner structure of electron beam source; additional support structures are not shown. A: snaked carbon heating element, B: ceramic base, C: LaB 6 disk, biasable to 4 kv, D: ceramic spacers, E: biasable grid, F: ceramic spacers, G: biasable grid, H: top ceramic ring. which in turn radiatively heats the ceramic disk and the LaB 6 disk. The emission current of the LaB 6 is a strong function of the temperature. Control over the beam density n b is possible by adjusting the DC heating power applied to the carbon heating element. Two grids are positioned in front of the LaB 6 disk, separated by insulating ceramic rings. Each grid and 4

5 Plasma Phys. Control. Fusion 9 (17) 1416 Figure 4. (a) Time series of beam source voltage (blue) and total beam current (red) emitted by the LaB6 disk. (b) Time series of fluctuations in the transverse magnetic field normalized to the local background field. (c) Spectrogram of the time series, showing a broadband emissions in an upper band and a lower band. (d) Power spectrum averaged over the last μs of the beam pulse. Plasma and beam parameters: ωpe /Ωe = 9.6, nb /n =.1% and v/c =.11 at 3 pitch angle. injected with finite pitch angle with energies in kev range. The background plasma density n which controls the factor ωpe /Ωe is varied by choosing the start time of the experiment during the density decay of the afterglow plasma. The ratio Bw /B, closely related to the ratio nb /n, is controlled either by varying the plasma density n at fixed beam density nb or vice versa. The magnetic field profile is adjusted by controlling the current through the external electromagnets of the LAPD device. the LaB6 are biasable independently. The grids serve the purpose of preventing the background plasma from entering the beam source. The outer grid is in contact with the background plasma and is held at floating potential which shields most plasma electrons from entering the source. The middle grid is biased positive to repel plasma ions. The electrons emitted by the LaB6 disk are accelerated by applying a large negative kv bias between the LaB6 disk and the machine wall. The potential difference between the machine wall and the front of the beam source, i.e. the floating grid, is on the order of a few Volt, negligible compared to the kv bias, which means the full acceleration of the electrons occurs within the beam source. The electrons therefore leave the beam source with the programmed kev energy. The source can be safely operated with 1 μs pulses at voltages up to 4 kv, and beam cur rents of a few Amperes. The beam source is angled to 3 or 4 degrees with respect to the magnetic field in order to provide sufficient free energy in the electron distribution for the cyclotron growth of whistler waves. The magnetic field at the beam source is restricted to the range of G, in order to allow accelerated electrons to escape the tilted beam source assembly. In the remainder of the paper the start of the electron beam pulse is taken as t = and the location of the electron beam source as z =. It is clear that the experimental setup enables us to satisfy the requirements enumerated in section. Beam electrons are 4. Emission types broadband and discrete frequency The experiment is performed for a range of plasma densities, beam densities and magnetic field profiles. An example for one particular set of parameters is shown in figure 4 []. The magnetic field is uniform and set to 6 G in this example (see figure 1 of [1]), the density is n = cm 3, corre sponding to ωpe /Ωe = 9.6. The beam is injected at a 3 degree pitch angle with 3 kev energy. Time traces of the beam voltage and beam current are displayed in figure 4(a). After a ramp-up period lasting about 1 μs the current and voltage reach steady state until the source is shut off. The beam voltage is 3 kev in the example, v corre sponding to a electron beam velocity of c =.11. The

6 Plasma Phys. Control. Fusion 9 (17) 1416 (a) -1-1 Y (cm) X (cm) Z (cm) Z (cm) (b) (c) Z (cm) 9 (d) Z (cm) Y (cm) - Y (cm) X (cm) - X (cm) Z (cm) Z (cm) Figure. 3D mode structure of different frequency components, (a) ω/ Ω e =.1, (b) ω/ Ω e =. and (c) ω/ Ω e =.3. Colors represent the B z component, while the vectors show the 3D direction of the magnetic field fluctuations. Panel (d) shows the dispersion relation for each frequency with the measured k and k indicated for each case. Figure 6. Measured values of k for each frequency for parameters of figure 4. Colors represent the wave power for each frequency component. Slanted lines indicate cyclotron and Landau resonances. beam current is A, which translates to an electron beam 7 density of nb = cm 3, which leads to a normalized beam density nb/ n =.1%. The beam source is on for 8 µ s Ω e 1. The time series of a component of the perpendicular magnetic field fluctuations and the associated spectrogram are shown in figures 4(b) (c). The electron beam spontaneously excites electromagnetic waves in the whistler wave frequency range, i.e. with frequencies Ω LH < ω <Ω. e The data in figure 4(b) is low pass filtered below Ω e since the focus of this paper is on the whistler wave frequency range. Amplitudes of the waves are in the mg range ( δ Bw/ B 1 ). The dynamic spectrogram is constructed by dividing the time series into consecutive and overlapping time segments of length τ, multiplying by a Hanning window and applying the Fourier transform to each time segment. In this analysis the time segments are τ =.8 μs long ( Ωe τ 8) and the frequency resolution is ω/ Ωe.1. The dynamic spectrogram in figure 4(c) display δb / δ B n, i.e. the power spectrum as a function of time, normalized to the power spectrum of the noise present prior to beam injection. This quantity is a measure of the wave amplification above the noise and brings out the low amplitude emissions better. The power spectrum shows broadband emissions ( ωω /.1) in two distinct bands, an upper band near.6 Ω e and a lower band near.3 Ω e, which is also clear from the power spectrum averaged over the last μs as shown in figure 4(d). Data was taken in two orthogonal data planes for the parameters of figure 4. A stationary probe was positioned less than one parallel wave length from the moving probe. The phase delay φ( x, ω) between the two probes is found using 6

7 Plasma Phys. Control. Fusion 9 (17) 1416 Figure 7. Measured power spectra for different beam energies at ωpe/ Ω e = 9.6 (top panel) and for different values of ωpe/ Ωe for a 3 kev beam (bottom panel). The beam pitch angle is 4 degrees. Linear theory predictions, based on cyclotron resonance, are indicated by the dashed lines. cross-correlation techniques. Together with the measured amplitude B( x, ω) on the moving probe, the 3D mode structure can be constructed as B( x, ω) exp( i φ( x, ω) i ωt). Figure shows the resulting mode structure for three different frequency components present in the magnetic field fluctuations, i.e. (a) ω/ Ω e =.1, (b) ω/ Ω e =. and (c) ω/ Ω e =.3, the latter corresponding to the peak in the power spectrum of figure 4(d). In the figures the beam electrons would be gyrating down from top to bottom, with a transverse crosssectional beam width of about 8 cm. The largest magnetic field fluctuations are seen near the beam, and phase fronts of the wave are centered on the beam. These waves were shown to be propagating near the resonance cone, as is clear from figure (d) which shows the theoretical dispersion curve for each frequency with the values for k and k taken from panels (a) (c) overplotted. Good agreement between theory and experiment is obtained. The strongest frequency components at ω/ Ω e =.3 propagate near the Gendrin angle, meaning that the group velocity is nearly parallel to the background magnetic field. In panels (a) (c) the phase fronts propagate radially inwards towards the beam. Waves near the resonance Figure 8. (a) Example spectrogram with discrete frequency chirping emission present, with ωpe/ Ω e =.6 and nb/ n = 1.8%. (b) Time trace of B x component. Vertical lines indicate extent of zoomed-in traces of panel (c). cone are backward propagating in the perpendicular direction. Therefore the group velocity is radially outwards and energy is transported away from the beam. The parallel propagation interestingly depends on the frequency. The waves at ω/ Ω e =.1 are co-propagating with the beam electrons while the waves at ω/ Ω e =.,.3 are counter-propagating. The values for k were obtained for all frequencies present in the power spectrum of figure 4(d). The result is organized in a plot of k versus ω, displayed in figure 6. Colors indicate the strength of each frequency component. Overplotted as slanted lines are the different waveparticle resonances as in equation (3), with n = 1,, 1. The strongest emissions occur for waves propagating counter to the beam electrons, and excited through the Doppler shifted cyclotron resonance. Strong emissions also occur through Landau resonance (co-propagating waves) which make up the low frequency shoulder in the power spectrum of figure 4(d). Theoretical predictions of the wave frequency for the excitation through Doppler shifted cyclotron resonance can be obtained by combining the whistler wave dispersion relation of equation () with the cyclotron resonance condition of equation (3) with n = 1. Making a simplifying assumption of parallel wave propagation ( θ = ), this yields 7

8 Plasma Phys. Control. Fusion 9 (17) 1416 Figure 9. Spectrograms of types of beam generated wave emissions, ranging from falling tones, hooks, simultaneous rising and falling tones, crossing and merging falling and rising tones. The fast electron energy is 3 kev for all cases, and ωpe/ Ω e =.6,.9,.6,.9,.9, and nb/ n (%) = 1.8, 1., 1.8, 1., 1. for panels (a) (e) respectively. ( 1 ω ) ω 3 ωpe v =. () Ω c Equation () shows that the determining parameters are the plasma density through ω pe / Ω e and the parallel beam speed v. Parameter scans were performed varying the beam energy and the background density for a 4 degree pitch angle beam. The measured spectra are shown in figure 7 with the predicted frequency overplotted as dotted lines. It is clear that the measured spectra closely follow the theoretical predictions for cyclotron resonance. When the plasma density is lowered further to the range ωpe/ Ωe a dramatic change in the wave activity occurs. The dynamic spectrograms reveal discrete frequency emissions with characteristic chirping, similar to chorus waves in space. An example is shown in figure 8. The dynamic spectrogram shows a clear falling tone, with a frequency chirp rate df 1 of = 8MHz µ s. Normalizing the chirp rate to the gyrofrequency gives = 1 which is similar to what dt dω / Ωe d Ωe t is typically observed in space [6 68]. The middle panel of figure 8 shows the time trace of the B x component. Zoomed-in time traces of all three magnetic field components during part of the chirp are shown in the lower panel. It should be noted that this data was obtained with a gradient in the background magnetic field, with scale length LB = = 4.8 B z zprobe m, which is larger by a factor of than the typical parallel wave length of whistler waves for the laboratory parameters (see figure 1 of [1]). Additional examples of the rich variety of whistler wave emissions from the laboratory experiment are shown in figure 9. Emission types include falling tones, rising tones, hooks, as well as crossing and merging chirps. The relevant plasma and beam parameters for each case are in the figure captions. For all cases the beam was injected at a 4 degree pitch angle at 3 kev. The magnetic field profile has a gradient with scale length LB = 4.8 m, the same as for figure 8. Data was acquired in a plane along the background magnetic field (x z plane), with a stationary reference probe positioned within one parallel wave length of the moving probe. Cross-correlation analysis was performed for the dataset with e 1 B 1 ( ) Figure 1. Mode structure of B x component for ω/ Ω e =.7 and for times during which chirps occur. Plasma and beam parameters are ωpe/ Ωe =.9; nb/ n (%) = 1., Eb = 3 kev. parameters ωpe/ Ω e =.9, and nb/ n ( %) = 1., for which panels (b), (d) and (e) of figure 9 show example spectrograms. Even though the chirp types are not the same, the start time and end time are reproducible ( 19 µ s< tchirp < 6 µ s) as well as the frequency range of the chirps (.6 < ωchirp/ Ω e<.8). The calculated cross-coherence is largest for those times and frequencies. Plotting the mode structure of the B x component for ω/ Ω e =.7 during the times of peak cross coherency, results in figure 1. The vertical line indicates the radial extent of the beam electrons, whereas the slanted line indicates how the wave fronts should be tilted for whistler waves propagating near the resonance cone for a frequency ω/ Ω e =.7. The whistler wave in this case is co-propagating with the beam electrons in the parallel direction. The measured k matches well with the value expected for Landau resonance of the wave with the electron beam. Chorus-like discrete frequency whistler waves as in figure 9 are only observed under specific conditions, i.e. ωpe/ Ωe 4, nb/ n 1%. This is similar to what is observed in space. A statistical analysis of five years of the Themis 8

9 Plasma Phys. Control. Fusion 9 (17) 1416 spacecraft data [] showed that the rising and falling tones predominantly occur for ratios of ω pe / Ω e between and 6. The absence of discrete frequency emissions at high density in the experiment could not only be attributed to ωpe/ Ω e but could also be due to the lower relative beam density nb/ n, since in the linear regime discrete emissions are not expected. It was not possible to keep nb/ n fixed at the higher plasma densities because of arcing inside the beam source. Instead n was varied at fixed n b, thereby affecting both ω pe / Ω e and nb/ n. It is therefore not clear yet if ωpe/ Ω e is the determining factor in the experiment. In the experiment discrete frequency modes are also observed near ω/ Ω e = 1., for less restrictive ranges of ω pe / Ω e and nb/ n. These modes will be reported elsewhere.. Conclusions In conclusion, an overview of results from a laboratory simulation of chorus wave excitation has been detailed. Chorus waves have been observed in space for decades; the nonlinear excitation of these waves by energetic electrons is however still an area of active research. The laboratory experiment is designed to closely mimic the scaled plasma parameters observed in the inner magnetosphere, and shed light on the excitation of discrete frequency whistler waves. It was observed that a rich variety of whistler wave emissions is excited by a gyrating electron beam. The properties of the whistler emissions depend strongly on plasma density, beam density and magnetic field profiles. In the future, detailed quantitative comparisons with theory and space observations will be done. Measurements of the electron distribution function, and how it evolves during the chirping, will be attempted. Acknowledgments The authors wish to thank G J Morales and T A Carter for insightful discussions. 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