Ray-tracing WKB analysis of Whistler waves in non-uniform magnetic fields applied to space thrusters

Cardinali, A.; Melazzi, Davide; Manente, Marco; Pavarin, Daniele

doi:10.1088/0963-0252/23/1/015013

Cited by 18 publications

(14 citation statements)

References 29 publications

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“…The expression of these coefficients can be found in Cardinali et al. (2014). Equation (2.4) is employed as follows: we impose , , , and we solve the dispersion relation for an interval of ; if the calculated is real than the wave is propagative, otherwise not.…”

Section: Methodsmentioning

confidence: 99%

“…Moreover, the effects of the magnetostatic field inhomogeneities on the power deposition phenomenon can be interpreted by analysing the dispersion relation reported in (2.4) (Cardinali et al. 2014). In fact, in the centre of the discharge, where the magnetostatic field is almost homogeneous and axial, the interval of propagative EM waves (expressed in terms of axial wavenumber ) is almost constant along the discharge radius (see figure 10 a ).…”

Section: Mono-dimensional Analysismentioning

confidence: 99%

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Study on the influence of the magnetic field geometry on the power deposition in a helicon plasma source

2019

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We have numerically studied how an actual confinement magnetostatic field affects power deposition in a helicon source. We have solved the wave propagation by means of two electromagnetic solvers, namely: (i) plaSma Padova Inhomogeneous Radial Electromagnetic solver (SPIREs), a mono-dimensional finite-difference frequency-domain code, and (ii) Advanced coDe for Anisotropic Media and ANTennas (ADAMANT), a full-wave three-dimensional tool based on the method of moments. We have computed the deposited power spectrum with SPIREs, power deposition profile with ADAMANT and the antenna impedance with both codes. First we have verified the numerical accuracy of both SPIREs and ADAMNT. Then, we have analysed two configurations of magnetostatic field, namely produced by Maxwell coils, and Helmholtz coils. For each configuration we have studied three cases: (i) low density $n=10^{17}~\text{m}^{-3}$ and low magnetic field $B_{0}=250$ G; (ii) medium density $n=10^{18}~\text{m}^{-3}$ and medium magnetic field $B_{0}=500$ G; (iii) high density $n=10^{19}~\text{m}^{-3}$ and high magnetic field $B_{0}=1000$ G. We have found that the Maxwell coil configuration does not produces significant changes in the deposited power phenomenon with respect to a perfectly uniform and axial magnetostatic field. While the Helmholtz coil configuration can lead to a power spectrum peaked near the axis of the discharge.

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Section: Methodsmentioning

confidence: 99%

Section: Mono-dimensional Analysismentioning

confidence: 99%

Study on the influence of the magnetic field geometry on the power deposition in a helicon plasma source

2019

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“…2012; Cardinali et al. 2014; Fabris et al. 2015), for the detailed design and optimization of plasma thrusters of the helicon type (Manente et al.…”

Section: Introductionmentioning

confidence: 99%

Enhanced biDimensional pIc: an electrostatic/magnetostatic particle-in-cell code for plasma based systems

Gallina¹,

Magarotto

Manente³

et al. 2019

J. Plasma Phys.

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EDI (enhanced biDimensional pIc) is a two-dimensional (2-D) electrostatic/magnetostatic particle-in-cell (PIC) code designed to optimize plasma based systems. The code is built on an unstructured mesh of triangles, allowing for arbitrary geometries. The PIC core is comprised of a Boris leapfrog scheme that can manage multiple species. Particle tracking locates particles in the mesh, using a fast and simple priority-sorting algorithm. A magnetic field with an arbitrary topology can be imposed to study the magnetized particle dynamics. The electrostatic fields are then computed by solving Poisson’s equation with a a finite element method solver. The latter is an external solver that has been properly modified in order to be integrated into EDI. The major advantage of using an external solver directly incorporated into the EDI structure is its strong flexibility, in fact it is possible to couple together different physical problems (electrostatic, magnetostatic, etc.). EDI is written in C, which allows the rapid development of new modules. A big effort in the development of the code has been made in optimization of the linking efficiency, in order to minimize computational time. Finally, EDI is a multiplatform (Linux, Mac OS X) software.

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“…12 Ray tracing studies have been done for wave propagation in the Earth's magnetic dipole field 13 and for wave injection along expanding field lines of plasma thrusters. 14 Experiments on cyclotron absorption have been done in several laboratory experiments. [15][16][17] However, the topic of wave propagation in highly nonuniform magnetic fields (B=jrBj < k) has received little attention since it is not amenable to ray tracing.…”

Section: Introductionmentioning

confidence: 99%

“…Such predictions cannot be made for whistler modes in lunar crustal magnetic fields 35 or for low frequency whistlers at the bowshock 36 or near reconnection regions. 37,38 Nonuniform magnetic fields also exist in the exhaust region of helicon thrusters 14,16,39 or toroidal plasma devices [39][40][41][42] with the focus on plasma production rather than wave refraction. Refraction in nonuniform magnetic fields destroys the cylindrical geometry of helicons.…”

Section: Introductionmentioning

confidence: 99%

Whistler modes in highly nonuniform magnetic fields. III. Propagation near mirror and cusp fields

Stenzel

Urrutia

2018

Physics of Plasmas

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The properties of helicon modes in highly nonuniform magnetic fields are studied experimentally. The waves propagate in an essentially unbounded uniform laboratory plasma. Helicons with mode number m ¼ 1 are excited with a magnetic loop with dipole moment across the dc magnetic field. The wave fields are measured with a three-component magnetic probe movable in three orthogonal directions so as to resolve the spatial and temporal wave properties. The ambient magnetic field has the topology of a mirror or a cusp, produced by the superposition of a uniform axial field B 0 and the field of a current-carrying loop with the axis along B 0. The novel finding is the reflection of whistlers by a strong mirror magnetic field. The reflection arises when the magnetic field changes on a scale length shorter than the whistler wavelength. The simplest explanation for the reflection mechanism is the strong gradient of the refractive index which depends on the density and magnetic field. More detailed observations show that the incident wave splits when the k vector makes an angle larger than 90 with respect to B 0 which produces a parallel phase velocity component opposite to that of the incident wave. The reflection coefficient has been estimated to be close to unity. Interference between reflected and incident waves creates nodes in which the whistler mode becomes linearly polarized. When the magnetic field topology is that of a reversed field configuration (FRC), the incident wave is absorbed near the three-dimensional (3D) magnetic null point which prevents wave reflections. However, waves outside the separatrix are not absorbed and continue to propagate around the null point. When waves are excited inside the FRC, their polarization and helicon mode are reversed. Implications of these observations on research in space plasmas and helicon sources are pointed out.

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Ray-tracing WKB analysis of Whistler waves in non-uniform magnetic fields applied to space thrusters

Cited by 18 publications

References 29 publications

Study on the influence of the magnetic field geometry on the power deposition in a helicon plasma source

Study on the influence of the magnetic field geometry on the power deposition in a helicon plasma source

Enhanced biDimensional pIc: an electrostatic/magnetostatic particle-in-cell code for plasma based systems

Whistler modes in highly nonuniform magnetic fields. III. Propagation near mirror and cusp fields

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