Abstract
Linear mode conversion (LMC) is the linear transfer of energy from one wave mode to another in an inhomogeneous plasma. It is relevant to laboratory plasmas and multiple solar system radio emissions, such as continuum radiation from planetary magnetospheres and type II and III radio bursts from the solar corona and solar wind. This paper simulates LMC of waves defined by warm, magnetized fluid theory, specifically the conversion of Langmuir/zmode waves to electromagnetic (EM) radiation. The primary focus is the calculation of the energy and power conversion efficiencies for LMC as functions of the angle of incidence θ of the Langmuir/zmode wave, temperature , adiabatic index γ, and orientation angle ϕ between the ambient density gradient and ambient magnetic field in a warm, unmagnetized plasma. The ratio of these efficiencies is found to agree well as a function of θ, γ, and β with an analytical relation that depends on the group speeds of the Langmuir/z and EM wave modes. The results demonstrate that the energy conversion efficiency ϵ is strongly dependent on , ϕ and θ, with and . The power conversion efficiency , on the other hand, is independent of but does vary significantly with θ and ϕ. The efficiencies are shown to be maximum for approximately perpendicular density gradients ( ) and minimal for parallel orientation ( ) and both the energy and power conversion efficiencies peak at the same θ.
We acknowledge funding from the Australian Research Council; the School of Physics at the University of Sydney; NASA grants NNH09AM53I, NNH09AK63I, and NNH11AQ46I; NSF grant ATM0902730; and DOE contract DEAC0209CH11466. We also thank D. B. Melrose for helpful discussions.
I. INTRODUCTION
II. THEORETICAL MODEL
A. Simulations
B. Analytical theory
1. Derivation of warm fluid dispersion relation
2. Derivation of kinetic dispersion relation
3. Energy and power conversion efficiencies
III. RESULTS
A. Density gradient parallel to ()
B. Varying magnetic field orientation ϕ for constant
C. Varying magnetic field orientation ϕ and varying
IV. DISCUSSION AND FUTURE APPLICATIONS
V. CONCLUSIONS
Key Topics
 Plasma waves
 64.0
 Energy efficiency
 38.0
 Magnetic fields
 19.0
 Magnetized plasmas
 12.0
 Plasma electromagnetic waves
 11.0
H01F1/44
Figures
Schematic illustration of the simulation domain reproduced from Ref. ^{ 25 } : Langmuir/zmode waves are generated in region II, propagate through region III, and encounter an increasing density gradient in region IV. The plasma is assumed to be homogeneous in regions and inhomogeneous in region IV. Additional damping is imposed in region I. Here .
Schematic illustration of the simulation domain reproduced from Ref. ^{ 25 } : Langmuir/zmode waves are generated in region II, propagate through region III, and encounter an increasing density gradient in region IV. The plasma is assumed to be homogeneous in regions and inhomogeneous in region IV. Additional damping is imposed in region I. Here .
Spatial dependence of the real part of the x, y, and z electric and magnetic wave fields (in arbitrary units) in region III of Figure 1 , where is in the z direction. Distances are measured in units of the input wavelength . This simulation is for , , , and . Note the different scales on the ordinate axes.
Spatial dependence of the real part of the x, y, and z electric and magnetic wave fields (in arbitrary units) in region III of Figure 1 , where is in the z direction. Distances are measured in units of the input wavelength . This simulation is for , , , and . Note the different scales on the ordinate axes.
Power spectra of the complex electric (top row) and magnetic (bottom row) fields from Figure 2 , in arbitrary units, in the x, y, and z directions (left to right), as functions of wave number k_{z} ( ). These are for an incoming ( ) Langmuir/z wave with (green dashed lines) for for , , and . The outgoing ( ) Langmuir/z waves have (blue dashed lines) while the radio waves have (red dashed lines). Note the different scales on the ordinate axes.
Power spectra of the complex electric (top row) and magnetic (bottom row) fields from Figure 2 , in arbitrary units, in the x, y, and z directions (left to right), as functions of wave number k_{z} ( ). These are for an incoming ( ) Langmuir/z wave with (green dashed lines) for for , , and . The outgoing ( ) Langmuir/z waves have (blue dashed lines) while the radio waves have (red dashed lines). Note the different scales on the ordinate axes.
Energy and power conversion efficiencies as functions of q and θ for different , , and : (a) , (b) ) on logarithmic scales, (c) , and (d) . Colour coding is for different (red), (green), (blue). Curves for different , and 3 go from lowest to highest in (a) and left to right in (b) and (d).
Energy and power conversion efficiencies as functions of q and θ for different , , and : (a) , (b) ) on logarithmic scales, (c) , and (d) . Colour coding is for different (red), (green), (blue). Curves for different , and 3 go from lowest to highest in (a) and left to right in (b) and (d).
Scaled energy and power conversion efficiencies Σ and , respectively, as functions of q and scaled Θ for differing , based on Eqs. (38) and (40) and scaled against the results for and : (a) , (b) , (c) , and (d) . The colours, values of γ, and simulation parameters are as for Figure 4 .
Scaled energy and power conversion efficiencies Σ and , respectively, as functions of q and scaled Θ for differing , based on Eqs. (38) and (40) and scaled against the results for and : (a) , (b) , (c) , and (d) . The colours, values of γ, and simulation parameters are as for Figure 4 .
Energy and power conversion efficiencies as functions of q and θ for different ϕ, but constant , , , and : (a) , (b) ), (c) , and (d) . Colour coding is for different ϕ: (red), (blue), (green), (orange), and (purple).
Energy and power conversion efficiencies as functions of q and θ for different ϕ, but constant , , , and : (a) , (b) ), (c) , and (d) . Colour coding is for different ϕ: (red), (blue), (green), (orange), and (purple).
Scaled energy and power conversion efficiencies E and E_{s} as functions of q and Θ for different , based on Eqs. (37)–(40) and scaled to , , and : (a) , (b) , (c) , and (d) scaled with Eqs. (37) and (35) to . The colours and simulation parameters are as for Figure 6 .
Scaled energy and power conversion efficiencies E and E_{s} as functions of q and Θ for different , based on Eqs. (37)–(40) and scaled to , , and : (a) , (b) , (c) , and (d) scaled with Eqs. (37) and (35) to . The colours and simulation parameters are as for Figure 6 .
Energy and power conversion efficiencies as functions of q and θ for differing , and β, and : (a) , (b) ), (c) , and (d) . Colour coding is for different ϕ: (red), (blue), (green), (orange), and (purple). Linestyles are for different values: (solid line), (dotted line), and (dashed line).
Energy and power conversion efficiencies as functions of q and θ for differing , and β, and : (a) , (b) ), (c) , and (d) . Colour coding is for different ϕ: (red), (blue), (green), (orange), and (purple). Linestyles are for different values: (solid line), (dotted line), and (dashed line).
Scaled energy and power conversion efficiencies Σ and as functions of q and Θ for differing , and β, based on Eqs. (37)–(40) and scaled to , and : (a) , (b) , (c) , and (d) . The colours, linestyles, and simulation parameters are as for Figure 8 .
Tables
Estimates of the temperature, , and energy conversion efficiencies in various regions in the solar system.
Estimates of the temperature, , and energy conversion efficiencies in various regions in the solar system.
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