<p>Theoretical studies of dusty plasmas have been performed by focusing attention principally on collective phenomena and on grain motion. This thesis consists of a collection of seven published papers that explore both the collective behavior of a complex plasma system as well as the dynamics of grains in plasmas. In paper 1, a mechanism that explains the energy gain which leads to the self excited grain oscillations is theoretically formulated. The newly developed mechanism explains the observed self excited oscillations through the coupling of plasma sheath fluctuations with the electrostatic force, which holds the dust grain. In paper 2, theoretical and simulation studies have been conducted to study the vertical oscillations of dust grains that are levitated in plasma sheaths, under low pressure conditions. The oscillations were driven either by an external force or by a plasma number density modulation. The proposed model gives a full picture of the dust grains dynamics and is capable of successfully explaining the experimental observations. Paper 3 explores both theoretically and numerically the origin of the nonlinearities that lead to the observed oscillation resonances. The feature of the confining potential well which traps the grain, the influence of an electrode voltage modulation on the trapping well, and hence on the grain dynamics, and the resulting nonlinear resonances are analyzed in detail. The numerical simulations presented successfully reproduce a broad range of dynamical phenomena, including the self excited oscillations, for a range of different parameters. Paper 4 is dedicated to the analysis of the propagation of Dust Acoustic Waves (DAW) in a medium with an equilibrium dust density distribution. It has been theoretically shown that only some harmonics of the dust density distribution will influence the propagation of the DAW, thus modifying its frequency. Paper 5 presents a theoretical and numerical analysis of the excitation of higher harmonics of electrostatic dust cyclotron waves. The instability is driven by the ion and electron currents flowing along the magnetic field. The dispersion relation and the wave instability conditions have been derived, and a detailed numerical analysis has been performed. In Paper 6, we explore theoretically some cross field instabilities of low frequency, long wavelength electrostatic modes in fully and weakly ionized plasmas. It is shown that in a magnetoplasma with a transverse equilibrium dc electric field, the energy associated with the cross field motion of the plasma particles can be coupled to low frequency electrostatic waves. Paper 7 explores the properties and instabilities of low frequency electrostatic waves propagating in a current carrying magnetoplasma with equilibrium density and field aligned ion flow with a transverse gradient. The paper contains previous results as limiting cases, together with additional instabilities related to the equilibrium plasma density distribution. </p>

Theoretical studies of dusty plasmas have been performed by focusing attention principally on collective phenomena and on grain motion. This thesis consists of a collection of seven published papers that explore both the collective behavior of a complex plasma system as well as the dynamics of grains in plasmas. In paper 1, a mechanism that explains the energy gain which leads to the self excited grain oscillations is theoretically formulated. The newly developed mechanism explains the observed self excited oscillations through the coupling of plasma sheath fluctuations with the electrostatic force, which holds the dust grain. In paper 2, theoretical and simulation studies have been conducted to study the vertical oscillations of dust grains that are levitated in plasma sheaths, under low pressure conditions. The oscillations were driven either by an external force or by a plasma number density modulation. The proposed model gives a full picture of the dust grains dynamics and is capable of successfully explaining the experimental observations. Paper 3 explores both theoretically and numerically the origin of the nonlinearities that lead to the observed oscillation resonances. The feature of the confining potential well which traps the grain, the influence of an electrode voltage modulation on the trapping well, and hence on the grain dynamics, and the resulting nonlinear resonances are analyzed in detail. The numerical simulations presented successfully reproduce a broad range of dynamical phenomena, including the self excited oscillations, for a range of different parameters. Paper 4 is dedicated to the analysis of the propagation of Dust Acoustic Waves (DAW) in a medium with an equilibrium dust density distribution. It has been theoretically shown that only some harmonics of the dust density distribution will influence the propagation of the DAW, thus modifying its frequency. Paper 5 presents a theoretical and numerical analysis of the excitation of higher harmonics of electrostatic dust cyclotron waves. The instability is driven by the ion and electron currents flowing along the magnetic field. The dispersion relation and the wave instability conditions have been derived, and a detailed numerical analysis has been performed. In Paper 6, we explore theoretically some cross field instabilities of low frequency, long wavelength electrostatic modes in fully and weakly ionized plasmas. It is shown that in a magnetoplasma with a transverse equilibrium dc electric field, the energy associated with the cross field motion of the plasma particles can be coupled to low frequency electrostatic waves. Paper 7 explores the properties and instabilities of low frequency electrostatic waves propagating in a current carrying magnetoplasma with equilibrium density and field aligned ion flow with a transverse gradient. The paper contains previous results as limiting cases, together with additional instabilities related to the equilibrium plasma density distribution.

La problématique de génération de champs magnétiques quasi-statiques intenses constitue un défi pour la physique de l’interaction laser-plasma. Proposé il y a 30 ans, l’utilisation de cibles "boucles" irradiées par laser se distinguent par leur design compact ne nécessitant aucune génération de courant pulsé en plus de la puissance laser et ont dévoilé récemment leur grand potentiel.Ce travail de thèse s’attache à la caractérisation des phénomènes physiques et au développement de cette technique. On a ainsi montré la génération de forts champs magnétiques quasi-statiques par interaction laser-matière (500 J, durée laser de 1 ns et intensité ~10^17 W/cm^2) atteignant une amplitude de plusieurs centaines de Teslas pendant 2 à 3 ns. L'évolution temporelle et la distribution spatiale des champs magnétiques ont été mesurés par trois diagnostics indépendants : sondes B-dot, rotation de Faraday et défléctométrie de protons. La caractérisation des mécanismes physiques sous-jacents ont aussi fait appel à des diagnostics de rayonnements X de la région irradiée par laser ainsi qu’à des mesures d’ombroscopie optique du fil de la boucle en expansion.Une application de ces champs au guidage magnétique d’électrons relativistes dans la matière dense a permis d'ouvrir de nouvelles perspectives au transport de hautes densités d’énergies dans la matière. En effet, en laissant suffisamment de temps pour que le champ magnétique pénètre dans la cible dense, une amélioration d’un facteur 5 de la densité d’énergie portée par les électrons après 50 µm de propagation a été mise en évidence.En outre, des décharges de courants intenses consécutives à l'irradiation par impulsion laser courtes (50 J, durée laser < 1 ps et intensité ~10^19 W/cm^2) ont été observées. Une imagerie protonique de la décharge a permis de mesurer la propagation d’une onde électromagnétique à des vitesses proches de la vitesse de la lumière. Cette onde d’une durée de ~ 40 ps a été utilisée comme lentille électromagnétique pour focaliser et sélectionner sur une bande étroite d'énergie un faisceau de protons de plusieurs MeV (jusqu’à 12 MeV) passant dans la boucle.Les résultats de ces différentes mesures et applications expérimentales ont été par ailleurs confrontées à des simulations et à des modèles analytiques.Les applications de cette thèse se déploient sur des aspects comme :- la fusion par confinement inertiel, en guidant des faisceaux d'électrons relativistes jusqu'au cœur de la capsule de combustible, tout en confinant les particules qui y déposent leur énergie ainsi que celles créées par les réactions de fusion nucléaire;- l'astrophysique et la planétologie de laboratoire, en générant des sources secondaires de particules énergétiques ou de rayonnement afin de porter la matière dense a de très hautes températures (matière tiède et dense), ou en magnétisant des plasmas pour reproduire des phénomènes astrophysiques à plus petite échelle au laboratoire;- et enfin le contrôle de faisceaux de particules chargées dans le vide pour le développement de sources laser dans le cadre d'applications s'effectuant à distance de la source notamment en science, dans l'industrie, ou même en médecine. / The problem of strong quasi-static magnetic field generation is a challenge in laser-plasma interaction physics. Proposed 30 years ago, the use of the laser-driven capacitor-coil scheme, which stands out for its compact design while not needing any additional pulsed power source besides the laser power, only recently demonstrated its potential.This thesis work aims at characterizing the underlying physics and at developing this scheme. We demonstrated the generation of strong quasi-static magnetic fields by laser (500 J, 1 ns-duration and ~10^17 W/cm^2 intensity) of several hundreds of Teslas and duration of 2-3 ns. The B-field space- and time-evolutions were characterized using three independent diagnostics: B-dot probes, Faraday rotation and proton-deflectometry). The characterization of the underlying physical processes involved also X-ray diagnostics of the laser-irradiated zone and optical shadowgraphy of the coil rod expansion.A novel application of externally applied magnetic fields to guide relativistic electron beam in dense matter has been carried out and the obtained results set the ground for improved high-energy-density transport in matter. Indeed, allowing sufficient time for the dense target magnetization, a factor 5 improvement of the electron energy-density flux at 50µm-depth was evidenced.Besides, the generation of high discharge currents consecutive to short laser pulse irradiation (50 J, <1 ps-duration and ~10^19 W/cm^2 intensity) was also pointed out. Proton imaging of the discharge permitted to measure the propagation of an electromagnetic wave at a velocity close to the speed of light. This wave, of ~40ps-duration, was used as an electromagnetic lens to focalize and energy-select a narrow energy range within a multi-MeV proton beam (up to 12 MeV) passing through the coil.All-above experimental measurements and application results were thoroughly compared to both computer simulations and analytic modeling.The applications of this thesis work in a near future will concern:- inertial confinement fusion, by guiding relativistic electron beams up to the dense core nuclear fuel, and by confining particles depositing their energy in it, or even those resulting from the fusion reactions;- laboratory planetology and astrophysics, by generating secondary sources of energetic particles and radiation to reach the warm-dense-matter state or by magnetizing plasmas to reproduce astrophysical phenomena in scaled experiments;- and finally, the control of charged particle beams in vacuum, useful in particular for the development of laser-driven sources for distant applications in science, industry or even medecine.

A white dwarf is most likely the end stage of a low mass star like our Sun, which results when the parent star consumes all the hydrogen in its core, thus bringing fusion to a halt. It is a dense and compact object, where the inward gravitational pull is balanced by the outward pressure arising due to the motion of its constituent degenerate electrons. The theory of non-magnetized and non-rotating white dwarfs was formulated extensively by S. Chandrasekhar in the 1930s, who also proposed a maximum possible mass for this objects, known as the Chandrasekhar limit (Chandrasekhar 1935)1. White dwarfs are believed to be the progenitors of extremely bright explosions called type Ia supernovae (SNeIa). SNeIa are extremely important and popular astronomical events, which are hypothesized to be triggered in white dwarfs having mass close to the famous Chandrasekhar limit ∼ 1.44M⊙. The characteristic nature of the variation of luminosity with time of SNeIa is believed to be powered by the decay of 56Ni to 56Co and, finally, to 56Fe. This feature, along with the consistent mass of the exploding white dwarf, is deeply linked with their utilization as “standard candles” for cosmic distance measurement. In fact, SNeIa measurements were instrumental in establishing the accelerated nature of the current expansion of the universe (Perlmutter et al. 1999). However, several recently observed peculiar SNeIa do not conform to this traditional explanation. Some of these SNeIa are highly over-luminous, e.g. SN 2003fg, SN 2006gz, SN 2007if, SN 2009dc (Howell et al. 2006; Scalzo et al. 2010), and some others are highly under-luminous, e.g. SN 1991bg, SN 1997cn, SN 1998de, SN 1999by, SN 2005bl (Filippenko et al. 1992; Taubenberger et al. 2008). The luminosity of the former group of SNeIa implies a huge Ni-mass (often itself super-Chandrasekhar), invoking highly super-Chandrasekhar white dwarfs, having mass 2.1 − 2.8M⊙, as their most plausible progenitors (Howell et al. 2006; Scalzo et al. 2010). On the other hand, the latter group produces as low as ∼ 0.1M⊙ of Ni (Stritzinger et al. 2006), which rather seem to favor sub-Chandrasekhar explosion scenarios. In this thesis, as the title suggests, we have endeavored to establish the existence of exotic, super- and sub-Chandrasekhar limiting mass white dwarfs, in order to explain the aforementioned peculiar SNeIa. This is an extremely important puzzle to solve in order to comprehensively understand the phenomena of SNeIa, which in turn is essential for the correct interpretation of the evolutionary history of the universe. Effects of magnetic field: White dwarfs have been observed to be magnetized, having surface fields as high as 105 − 109 G (Vanlandingham et al. 2005). The interior field of a white dwarf cannot be probed directly but it is quite likely that it is several orders of magnitude higher than the surface field. The theory of weakly magnetized white dwarfs has been investigated by a few authors, however, their properties do not starkly contrast with that of the non-magnetized cases (Ostriker & Hartwick 1968). In our venture to find a fundamental basis behind the formation of super-Chandrasekhar white dwarfs, we have explored in this thesis the impact of stronger magnetic fields on the properties of white dwarfs, which has so far been overlooked. We have progressed from a simplistic to a more rigorous, self-consistent model, by adding complexities step by step, as follows: • spherically symmetric Newtonian model with constant (central) magnetic field • spherically symmetric general relativistic model with varying magnetic field • model with self-consistent departure from spherical symmetry by general relativis-tic magnetohydrodynamic (GRMHD) numerical modeling. We have started by exploiting the quantum mechanical effect of Landau quanti-zation due to a maximum allowed equipartition central field greater than a critical value Bc = 4.414 × 1013 G. To begin with, we have carried out the calculations in a Newtonian framework assuming spherically symmetric white dwarfs. The primary ef-fect of Landau quantization is to stiffen the equation of state (EoS) of the underlying electron degenerate matter in the high density regime, and, hence, yield significantly super-Chandrasekhar white dwarfs having mass much & 2M⊙ (Das & Mukhopadhyay 2012a,b). Consequently, we have proposed a new mass limit for magnetized white dwarfs which may establish the aforementioned peculiar, over-luminous SNeIa as new standard candles (Das & Mukhopadhyay 2013a,b). We have furthermore predicted possible evo-lutionary scenarios by which super-Chandrasekhar white dwarfs could form by accretion on to a commonly observed magnetized white dwarf, by invoking the phenomenon of flux freezing, subsequently ending in over-luminous, super-Chandrasekhar SNeIa (Das et al. 2013). Before moving on to a more complex model, we have justified the assumptions in our simplistic model, in the light of various related physics issues (Das & Mukhopad-hyay 2014b), and have also clarified, and, hence, removed some serious misconceptions regarding our work (Das & Mukhopadhyay 2015c). Next, we have considered a more self-consistent general relativistic framework. We have obtained stable solutions of magnetostatic equilibrium models for white dwarfs pertaining to various magnetic field profiles, however, still in spherical symmetry. We have showed that in this framework, a maximum stable mass as high as ∼ 3.3M⊙ can be realized (Das & Mukhopadhyay 2014a). However, it is likely that the anisotropic effect due to a strong magnetic field may cause a deformation in the spherical structure of the white dwarfs. Hence, in order to most self-consistently take into account this departure from spherical symmetry, we have constructed equilibrium models of strongly magnetized, static, white dwarfs in a general relativistic framework, first time in the literature to the best of our knowledge. In order to achieve this, we have modified the GRMHD code XNS (Pili et al. 2014), to apply it in the context of white dwarfs. Interestingly, we have found that signifi-cantly super-Chandrasekhar white dwarfs, in the range ∼ 1.7 − 3.4M⊙, are obtained for many possible field configurations, namely, poloidal, toroidal and mixed (Das & Mukhopadhyay 2015a). Furthermore, due to the inclusion of deformation caused by a strong magnetic field, super-Chandrasekhar white dwarfs are obtained for relatively lower central magnetic field strengths (∼ 1014 G) compared to that in the simplistic model — as correctly speculated in our first work of this series (Das & Mukhopadhyay 2012a). We have also found that although the characteristic deformation induced by a purely toroidal field is prolate, the overall shape remains quasi-spherical — justifying our earlier spherically symmetric assumption while constructing at least some models of strongly magnetized white dwarfs (Das & Mukhopadhyay 2014a). Indeed more accurate and extensive numerical analysis seems to have validated our analytical findings. Thus, very interestingly, our investigation has established that magnetized white dwarfs can indeed have mass that significantly exceeds the Chandrasekhar limit, irre-spective of the origin of the underlying magnetic effect — a discovery which is not only of theoretical importance, but also has a direct astrophysical implication in explaining the progenitors of the peculiar, over-luminous, super-Chandrasekhar SNeIa. Effects of modified Einstein’s gravity: A large array of models has been required to explain the peculiar, over- and under- luminous SNeIa. However, it is unlikely that nature would seek mutually antagonistic scenarios to exhibit sub-classes of apparently the same phenomena, i.e., triggering of thermonuclear explosions in white dwarfs. Hence, driven by the aim to establish a unification theory of SNeIa, we have invoked in the last part of this thesis a modification to Einstein’s theory of general relativity in white dwarfs. The validity of general relativity has been tested mainly in the weak field regime, for example, through laboratory experiments and solar system tests. However, the question remains, whether general relativity requires modification in the strong gravity regime, such as, the expanding universe, the region close to a black hole and neutron star. For instance, there is evidence from observational cosmology that the universe has undergone two epochs of cosmic acceleration, the theory behind which is not yet well understood. The period of acceleration in the early universe is known as inflation, while the current accelerated expansion is often explained by invoking a mysterious dark energy. An alternative approach to explain the mysteries of inflation and dark energy is to modify the underlying gravitational theory itself, as it conveniently avoids involving any exotic form of matter. Several modified gravity theories have been proposed which are extensions of Einstein’s theory of general relativity. A popular class of such theories is known as f (R) gravity (e.g. see de Felice & Tsujikawa 2010), where the Lagrangian density f of the gravitational field is an arbitrary function of the Ricci scalar R. In the context of astrophysical compact objects, so far, modified gravity theories have been applied only to neutron stars, which are much more compact than white dwarfs, in order to test the validity of such theories in the strong field regime (e.g. Cooney et al. 2010; Arapoˇglu et al. 2011). Moreover, a general relativistic correction itself does not seem to modify the properties of a white dwarf appreciably when compared to Newtonian calculations. Our venture of exploring modified gravity in white dwarfs in this thesis, is a first in the literature to the best of our knowledge. We have exploited the advantage that white dwarfs have over neutron stars, i.e., their EoS is well established. Hence, any change in the properties of white dwarfs can be solely attributed to the modification of the underlying gravity, unlike in neutron stars, where similar effects could be produced by invoking a different EoS. We have explored a popular, yet simple, model of f (R) gravity, known as the Starobinsky model (Starobinsky 1980) or R−squared model, which was originally pro-posed to explain inflation. Based on this model, we have first shown that modified gravity reproduces those results which are already explained in the paradigm of general relativity (and Newtonian framework), namely, low density white dwarfs in this context. This is a very important test of the modified gravity model and is furthermore necessary to constrain the underlying model parameter. Next, depending on the magnitude and sign of a single model parameter, we have not only obtained both highly super-Chandrasekhar and highly sub-Chandrasekhar limiting mass white dwarfs, but we have also established them as progenitors of the peculiar, over- and under-luminous SNeIa, respectively (Das & Mukhopadhyay 2015b). Thus, an effectively single underlying the-ory unifies the two apparently disjoint sub-classes of SNeIa, which have so far hugely puzzled astronomers. To summarize, in the first part of the thesis, we have established the enormous significance of magnetic fields in white dwarfs in revealing the existence of significantly super-Chandrasekhar white dwarfs. These super-Chandrasekhar white dwarfs could be ideal progenitors of the peculiar, over-luminous SNeIa, which can, hence, be used as new standard candles of cosmic distance measurements. In the latter part of the thesis, we have established the importance of a modified theory of Einstein’s gravity in revealing both highly super- and highly sub-Chandrasekhar limiting mass white dwarfs. We have furthermore demonstrated how such a theory can serve as a missing link between the peculiar, super- and sub-Chandrasekhar SNeIa. Thus, the significance of the current thesis lies in the fact that it not only questions the uniqueness of the Chandrasekhar mass-limit for white dwarfs, but it also argues for the need of a modified theory of Einstein’s gravity to explain astrophysical observations.

In the present thesis, magnetization reversal in both out-of-plane and in-plane magnetized thin lms and in devices fabricated out of those lms are explored. Pt/Co/Pt stacks with ultrathin Co layer were in-estimated initially for understanding their magnetic properties in this thesis. These perpendicular magnetized systems are good candidates for magnetic hard disc drives due to their large anisotropy, which may allow miniaturization of magnetic data storage devices. The spin Hall e ect mediated current-induced magnetization reversal in patterned Pt/Co/Pt devices were extensively investigated. Investigation of the magnetization reversal by means of a current instead of a magnetic eld is necessary to explore the possibilities of solid state magnetic memory devices. This is the primary motivation behind the investigation of current-induced magnetization reversal in Pt/Co/Pt system, in this thesis. Another important proposal for magnetic data storage is the race track memory, where the domain walls separating magnetic domains (in in-plane or out-of-plane magnetized materials) are moved by using a current. This involves a great deal of understanding of the domain wall motion in Nano-conduits under applied magnetics ends, and currents and also its interaction with engineered geometrical features. In this thesis work, magnetic led-driven domain wall pinning and deepening experiments on in-plane magnetized nanowires of perm alloy were performed to un-distend this interaction and the e act of domain wall chirality. In chapter 1, a general introduction to di errant data storage technologies and the current progress in the leg of spintronic is presented. This will highlight a perspective of this thesis work with respect to the present day research in spintronic and magnetization reversal studies. In chapter 2, a basic background of magnetism using the micromag-netic framework is illustrated. A brief introduction to magnetic domain walls is also presented. The Landau-Lifshitz-Gilbert dynamical equation is discussed and some case studies applied to a single domain particle with uniaxial anisotropy under the effect of spin-orbit torque are illu trated. The basics of spin-orbit coupling leading to spin Hall e ect is also explain In chapter 3, most of the essential experimental tools along with their basic working principles are described. Extensive e orts have been in-vested in designing and building the experimental tools. These include custom designs of a sputter deposition system, an ultra-high vacuum chamber for pulsed laser ablation, a magneto-optic Kerr e ect magne-tometer, a Kerr imaging system and a magneto-transport setup. All of these experimental setups have been automated, details of which are brie y discussed in this chapter. The Kerr imaging system was designed to measure hysteresis loops, observe domain wall motion and to measure domain wall velocity under applied magnetic elds and electric current. The magneto-transport setup was used for studying the domain wall pinning and depinning experiments in permalloy nanowires. In chapter 4, the optimization process for obtaining perpendicular mag-netic anisotropy in Pt/Co/Pt lms is described. The spin reorientation transition with varying thickness of Co (from 1.5 nm down to 0.35 nm) was studied. The magnetization easy axis direction changes from in-plane to out-of-plane as the thickness of Co is reduced. The dependence of Curie temperatures of ultrathin Co lms, with thickness as low as 0.35 nm, on the underlayer Pt thickness and its crystallinity was studied in detail. The e act of Ta but err layer on the texture of the Pt lm, and on the Curie temperature of the Pt/Co/Pt system was evaluated. To gain further insight of the role of the bottom Pt/Co and the top Co/Pt interfaces, ultrathin Cu lbs were inserted at the respective interfaces, and the anisotropy and magnetization reversal behaviour of these lbs were investigated. In chapter 5, studies on current-induced magnetization reversal in mi-corn sized wires of Pt/Co/Pt trilete is presented. The spin Hall e act assisted spin-orbit torque was used to reversibly switch the magnetization of these devices with and without the help of an external magnetic led. Since both the top and bottom layers are Pt, any contribution from Rashia e act towards spin-orbit torque could be ignored. By preparing devices with unequal top and bottom Pt thicknesses, a net spin-orbit torque could be applied to the magnetization of the Co layer. The thickness gradient/induced anisotropy in the Co layer was utilized to experimentally investigate current-induced deterministic switching. Sin-gel domain simulations with spin-orbit torque were also carried out to understand the mechanism of deterministic switching of magnetization in Pt/Co/Pt devices. This study is expected to have made sign cant contributions and to open up the possibilities of further investigation in the studies of spin-orbit torque in Pt/Co/Pt systems for solid state magnetic memory devices. In chapter 6, magnetic led-induced reversal in systems with in-plane magnetic anisotropy is presented. Here the e act of the width of a Nanos-trip on the anisotropy of a soft magnetic material like perm alloy was in-estimated. By introducing a nucleation pad to one end of the perm alloy nanowire, a single domain wall was generated at the junction with apple-cation of a proper magnetic led sequence. This domain wall could be in-jested into the nanowire by a magnetic led and pinned at a geometrical constriction inside the nanowire. The statistics of domain wall pinning and deepening processes indicated two di errant types of domain walls involved in the reversal process. With the assistance of micro magnetic simulations the domain walls were ident end as vortex walls of di errant chirality’s. Thus the interaction of domain walls with a Nano constriction and its dependence on the chirality of domain walls are understood. In chapter 7, a brief summary of the results obtained during the course of investigations is presented. An outlook presented at the end will help the readers of this thesis to understand the important research problems in this area and their potential future aspects.

In a fusion plasma, the ions have to be heated to reach fusion relevant temperatures. One possibility is to launch an electromagnetic wave in the radio frequency band into the plasma. This wave can resonate with the ions at their cyclotron frequency and hence, the method is called ion cyclotron resonance heating. If the Larmor radius is of similar length scales as the wavelength, finite Larmor radius (FLR) effects are important. This introduces additional possible wave modes. To accurately predict the heating, simulations of these additional modes can be important. In order to describe the FLR effects in simulations, this work applies a Taylor expansion to second order in the perpendicular wavenumber of the dielectric tensor. In real space, the Taylor expansion corresponds to a series of spatial derivatives. These derivatives are implemented as weak-form contributions for a onedimensional finite element method (FEM)simulation. The approach is realized in a fork of the FEMIC code, coupling plasma physics in MATLAB with the FEM solver in COMSOL. The discretization of the FEM solver is adapted using a Helmholtz filter to provide the required degree of smoothness. Our approach proves successful to simulate FLR effects within the limitations caused by the modeling choices. We compare results with an all-order FLR method, showing good qualitative agreement. This work serves as a proof of concept to describe challenges on the way towards incorporation of second order FLR effects in twodimensional simulations in FEMIC. / I ett fusionsplasma måste jonerna värmas för att plasmat ska nå temperaturer relevanta för fusion. En möjlighet är att sända in en elektromagnetisk våg i radiofrekvensbandet i plasmat. Den vågen kan sedan resonera med jonerna vid deras cyklotronfrekvens, och därför kallas metoden för joncyklotronresonansuppvärmning. Om våglängden är jämförbar med Larmorradien blir ändliga Larmorradie-effekter viktiga. Detta möjliggör ytterligare typer av vågor. Det kan vara viktigt att simulera dessa typer av vågor för att förutsäga uppvärmningen på ett träffsäkert vis. I denna masteruppsats Taylorutvecklar vi den dielektriska tensorn till andra ordningen i det vinkelräta vågtalet för att beskriva hur FLR-effekter påverkar simuleringarna. I det reella rummet motsvarar Taylorutvecklingen en serie av rumsliga derivator. Dessa derivator implementeras sedan som bidrag på svag form i en endimensionell modell som löses med den finita elementmetoden (FEM). Metoden implementeras i FEMIC-koden, som kopplar plasmafysik i MATLAB med FEM-lösaren i COMSOL. Diskretiseringen av FEM anpassas med ett Helmholtzfilter för att få en tillräckligt slät funktion. Ansatsen visar sig kunna framgångrikt simulera FLR-effekter, med vissa förväntade begränsningar. Lösningen jämförs sedan med lösningen från en metod som tar hänsyn till FLR-effekter, men som inte är baserad på en serieuteckling. Vi finner god kvalitativ överensstämmelse. Detta arbete fungerar som en prototyp och ämnar att beskriva de utmaningar som kan uppstå vid implementation av FLR-effekter den tvådimensionella axisymmetriska versionen av FEMIC.