Cylindrical Magnetic Field Research Articles

KEEPING AN ELECTRON BEAM IN POTENTIAL WELL MAGNETIC SOLENOIDAL FIELD

An intense cylindrical magnetic field is considered in which potential well is created with the help of additional magnets. It is shown that the motion of electrons can be associated with model of three-dimensional oscillations in potential well. The results of numerical simulation of electron trajectories in gradient magnetic field with point secondary emission cathode located in the middle of the system are presented. The formation of the beam with energy of 55 keV in the radial and longitudinal directions during its transportation in solenoidal field with large gradient is considered. The operating modes of the gun are obtained, in which the particle experiences stable three-dimensional vibrations. The influence of the initial conditions during emission on the occurrence of oscillations is studied. It is shown that for the given electron energy and the fixed magnetic field, the parameter that determines the stability of particle motion is the polar angle of entry relative to the axis of the cylindrical magnetic field.

Realization of an optimized cylindrical uniform magnetic field coil via flexible printed circuit technology

Abstract The design and fabrication method of magnetic field coils with high uniformity is essential for atomic magnetometers. In this paper, a novel design strategy for cylindrical uniform coils is first proposed, which combines the target-field method (TFM) with an optimized slime mold algorithm (SMA) to determine optimal structure parameters. Then, the realization method for the designed cylindrical coil by using the flexible printed circuit (FPC) technology is presented. Compared with traditional fabrication methods, this method has advantages in excellent flexibility and bending property, making the coils easier to be arranged in limited space. Moreover, the manufacturing process of the FPC technology via a specific cylindrical uniform magnetic field coil is discussed in detail, and the successfully realized coil is well tested in a verification system. By comparing the uniformity performance of the experimental coil with the simulation one, the effectiveness of the FPC technology in producing cylindrical coils has been well validated.

A spectroscopic investigation of thermal instability for cylindrical equilibria with background flow

Context. Flows are omnipresent and govern the dynamics of plasma. Solar tornadoes are a class of apparently rotating prominences that might be formed by thermal instability. In spectroscopic studies on thermal instability, background flow is commonly neglected. Aims. We here determine the effect of background flow on thermal instability in cylindrical magnetic field configurations. How various parameters affect the distribution of eigenmodes in the magnetohydrodynamic (MHD) spectrum is also explored. We investigate whether discrete thermal modes exist. Methods. In an analytical study, we extended upon the literature by including a generic background flow in a cylindrical coordinate system. The non-adiabatic MHD equations are linearised, Fourier-analysed, and examined to understand how a background flow changes the continua. An approximate expression for discrete thermal modes is derived using a Wentzel-Kramers-Brillouin (WKB) analysis. The analytical results are then verified for a benchmark equilibrium using the eigenvalue code Legolas. The eigenfunctions of discrete thermal modes are visualised in 2D and 3D. Results. The thermal continuum is Doppler-shifted due to the background flow, just like the slow and Alfvén continua. Discrete modes are altered because the governing equations contain flow-related terms. An approximate expression to predict the appearance of discrete thermal modes based on the equilibrium parameters is derived. All analytical expressions match the numerical results. The distribution of the density perturbations of the discrete thermal modes is not a uniform or singular condensation, due to the shape of the eigenfunctions and the dependence of the assumed waveform on the coordinates and wavenumbers. A 3D visualisation of the total velocity field shows that the helical field is heavily influenced by the radial velocity perturbation. Conclusions. We derived analytic expressions for non-adiabatic MHD modes of a cylindrical equilibrium with background flow and verified them using a coronal equilibrium. However, the equations are valid for and can be applied in other astrophysical environments.

ELECTRON BEAMS IN THE GRADIENT MAGNETIC FIELD: CONTROL FOR CONVERTING LONGITUDINAL MOTION INTO TRANSVERSAL

The motion of electrons in the cylindrical magnetic field of the magnetron gun with a gradient-type potential is considered. The formation of a beam with an energy of 55 keV in such the magnetic field has been studied. It is found that in the selected field, the initial motion of electrons along the longitudinal axis is converted into radial motion. It is determined that such the transformation is due to the influence of the solenoidal magnetic field with large longitudinal gradient. The transformation of the longitudinal direction of motion into the transverse one is stable in the energy range of 20...55 keV of electrons and in the range of 5...55 mm of radial dimensions of the particle beam. The modes of operation of the gun, in which the particle undergoes a stable transformation of the direction of motion, are studied numerically. It is shown that for the given electron energy and the fixed magnetic field, the parameter that determines the rotation of particles is the magnetic field gradient at the boundary of the entry region. It is found that the rotation effect takes place for the range of radial beam sizes, which leads to particle focusing. The possibility is shown to control the vertical coordinate of a focused beam on the basis of field adjustment as the whole. Based on the model of electron flow motion, the characteristics of the resulting electron beam are considered. It is shown that the beam, having radial dimensions of 5...55 mm, is focused vertically on the section of 1 mm.

Natural convection and entropy generation of Fe3O4-H2O nanofluids in square cavities with cylindrical grooves under magnetic field

Heat dissipation is crucial for the device performance, including electronic components, lithium-ion battery, solar collectors. Natural convection is regarded as one of the important ways of heat dissipation. The natural convection and entropy generation of Fe3O4-H2O nanofluids in cavities were experimentally investigated, and some influence factors including various mass fractions (0%, 0.1%, 0.3%, 0.5%) and heating powers (6 W, 12 W, 18 W, 24 W) were analyzed in detail, combining with unique square cavities and magnetic fields together. There are six square cavities with different arrangements (aligned, staggered) and depth of cylindrical grooves (1 mm, 2 mm, 3 mm), and magnetic fields have three different directions (unilateral vertical, bilateral corresponding, bilateral staggered) and intensities (0.01 T, 0.02 T, 0.03 T). The experimental data demonstrated that the optimum square cavity and magnetic field are staggered arrangement, depth h= 3 mm and bilateral staggered vertical, intensity B= 0.03 T, respectively. The cylindrical grooves and magnetic field can help decrease the thermal resistance and enhance efficiency of convection heat transfer. And mass fraction and heating power can also improve heat transfer. Furthermore, the entropy generation ṠT in the square cavity was also derived and studied. The result is really meaningful and worthwhile for designing or optimizing heat transfer system.

ELECTRON BEAMS IN THE GRADIENT MAGNETIC FIELD: CONTROL FOR CONVERTING LONGITUDINAL MOTION INTO TRANSVERSAL

The motion of electrons in a cylindrical magnetic field with the gradient-type potential is considered. The motion of electrons in the cylindrical magnetic field with the gradient-type potential is considered. It is found that in the selected field, the initial motion of electrons along the longitudinal axis is converted into motion along the radius. It is determined that such the transformation is due to the action of a solenoidal magnetic field with large longitudinal gradient. The transformation of the longitudinal direction of motion into the transverse one turned out to be stable in the energy range of 20...55 keV of electrons and in the range of 5...50 mm of radial dimensions of the particle beam. The main dependences of the motion of the electron beam in the given solenoidal magnetic field are studied with the help of the software tool. The results of numerical simulation of electron trajectories in the gradient magnetic field with the circular secondary emission cathode located in the middle of the system are presented. To study the mechanism of stability with respect to magnetic field, two experimentally realized magnetic fields were used. Based on these two fields, arrays of additional 4 fields are numerically synthesized. For the set of 6 named fields, the operation of the gun, in which the particle undergoes the stable transformation of the direction of motion, is numerically studied. It is shown that for the given electron energy and the fixed magnetic field, the parameter that determines the rotation of the particles is the magnetic field gradient at the boundary of the entry region. It is found that the rotation effect takes place for the considered range of radial beam sizes, which leads to particle focusing. The possibility is shown to control the vertical coordinate of the focused beam on the basis of the field adjustment, thereby giving the interpretation of the pore dependence of the registration of electrons on the detector. The dependence of the formation of the final distribution of particles on the amplitude and gradient of the magnetic field along the axis of the system is studied. The results of numerical simulation on the motion of the electron beam are presented. Based on the model of electron flow motion, the characteristics of the resulting electron beam are considered. It is shown that the beam, having radial dimensions of 5...50 mm, is transformed and focused vertically on the area of 1 mm.

Soft Magnetic Properties and Electromagnetic Shielding Performance of Fe40Ni40B20 Microfibers

AbstractFe40Ni40B20 metallic glass is a key material among the many amorphous systems investigated thus far, owing to its high strength and appealing soft magnetic properties that make it suitable for use as transformer cores. In this study, Fe40Ni40B20 microfibers are fabricated down to 5 µm diameter. Three different melt–spinning wheel velocities: ≈51 m s−1, ≈59 m s−1, and ≈63 m s−1 (MG1, MG2, MG3) are used. Their fully amorphous structure is confirmed using X–ray diffraction, and differential scanning calorimetry (DSC) traces reveal a larger relaxation profile for the higher–quenched microfiber. Vibrating sample magnetometer measurements showed a higher saturation magnetization of 136 emug−1 for annealed metallic glass microfibers with a wheel velocity of 59.66 ms−1. Cylindrical magnetic field shields are obtained by aligning and wrapping the fibers around a cast. The observed anisotropic static field shielding behavior is in accordance with the microfibers' anisotropic nature. Composite samples are also produced by embedding the microfibers in an epoxy matrix to investigate their electromagnetic properties at GHz frequencies. Inclusion of the microfibers increase the composite's attenuation constant by 20 to 25 times, making it an ideal candidate for applications in the communications frequency range.

Radiation emitted from axion dark matter in a homogeneous magnetic field and possibilities for detection

We study the direct radiation excited by oscillating axion (or axion-like particle) dark matter in a homogenous magnetic field and its detection scheme. We concretely derive the analytical expression of the axion-induced radiated power for a cylindrical uniform magnetic field. In the long wave limit, the radiation power is proportional to the square of the B-field volume and the axion mass $m_a$, whereas it oscillate as approaching the short wave limit and the peak powers are proportional to the side area of the cylindrical magnetic field and $m_a^{-2}$. The maximum power locates at mass $m_a\sim\frac{3\pi}{4R}$ for fixed radius $R$. Based on this characteristic of the power, we discuss a scheme to detect the axions in the mass range $1-10^4$\,neV, where four detectors of different bandwidths surround the B-field. The expected sensitivity for $m_a\lesssim1\,\mu$eV under typical-parameter values can far exceed the existing constraints.

Self-generated magnetic field in plasma reconstructed by using inverse Abel transformation in proton radiography

The magnetic fields generated in plasmas have extensive influences on many processes of the inertial confinement fusion and the astrophysics. Therefore, the quantitative diagnosis of the magnetic field is quite essential. Proton radiography is a widely used experimental technique to diagnose the electric field or magnetic field in high-energy-density plasma. The effective explanation of the results of proton radiography depends on the reliability and availability of the inversion method. Traditional inversion methods can only provide one- or two-dimensional structure of the self-generated magnetic field. In this study, it is found that there is an Abel transformation relationship between the deflection velocity and the magnetic field with column symmetry, which allows us to reconstruct the three-dimensional structure of the magnetic field for the first time. We theoretically deduce the process of reconstructing the cylindrical magnetic field through proton radiography with the Abel inversion algorithm. The feasibility of this method is verified by numerical simulation as well. Based on this inversion method, we reanalyze the proton radiography experimental results of Li et al. (<ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://doi.org/10.1038/ncomms13081">2016 <i>Nat. Commun.</i> <b>7</b> 13081</ext-link>) on the self-generated magnetic field of plasma jets. The inversion results show that the maximum magnetic field intensity is about 1.9 times the traditional inversion results. We discuss a new proton radiography inversion method for the existence of magnetic fields with cylindrical symmetry in thiswork, which will contributes to an intensive understanding of the self-generated electromagnetic field and its spatiotemporal evolution related to the laser fusion and the laboratory astrophysics.

MODELING OF OSCILLATORY AND ROTARY TRAJECTORIES OF ELECTRONS IN GRADIENT MAGNETIC FIELD MAGNETRON GUN

The motion of electrons in cylindrical magnetic field with variable strength along the axis is considered. The formation of a beam with energy of 55 keV in the longitudinal direction during its transport in solenoidal magnetic field with large gradient has been studied. The bifurcation regimes of the dynamics of particles during their move-ment along the transport axis both forward to the target and back to the cathode region are considered. The operat-ing modes of the gun are obtained, in which the particle experiences the "bottleneck" effect and returns to the cath-ode region. It is shown that for given electron energy and fixed magnetic field, the parameter that determines the reflection of the particle is the polar angle of entry with respect to the axis of the cylindrical magnetic field. The re-sults of numerical simulation on the motion of the electron flow are presented.

Spatially Highly Resolved Solar-wind-induced Magnetic Field on Venus

Abstract The current work investigates the Venusian solar-wind-induced magnetosphere at a high spatial resolution using all Venus Express (VEX) magnetic observations through an unbiased statistical method. We first evaluate the predictability of the interplanetary magnetic field (IMF) during VEX’s Venusian magnetospheric transits and then map the induced field in a cylindrical coordinate system under different IMF conditions. Our mapping resolves structures on various scales, ranging from the ionopause to the classical IMF draping. We also resolve two recently reported structures, a low-ionosphere magnetization over the terminator, and a global “looping” structure in the near magnetotail. In contrast to the reported IMF-independent cylindrical magnetic field of both structures, our results illustrate their IMF dependence. In both structures, the cylindrical magnetic component is more intense in the hemisphere with an upward solar wind electric field (E SW) than in the opposite hemisphere. Under downward E SW, the looping structure even breaks, which is attributable to an additional draped magnetic field structure wrapping toward −E SW. In addition, our results suggest that these two structures are spatially separate. The low-ionosphere magnetization occurs in a very narrow region, at about 88°–95° solar zenith angle and 185–210 km altitude. A least-squares fit reveals that this structure is attributable to an antisunward line current with 191.1 A intensity at 179 ± 10 km altitude, developed potentially in a Cowling channel.

LONGITUDINAL TRAP OF ELECTRON BEAM IN POTENTIAL PIT MAGNETIC SOLENOIDAL FIELD

A two-mode cylindrical magnetic field is considered, the potential of which has a minimum. The object of this work is the study of the parameters of an electron beam when it moves in a solenoid field with the longitudinal trap formed by the magnetic field, and the construction of the computational model of the motion of an electron beam. The problem is posed of the stability of the motion of electrons in such solenoid magnetic field. The possibility of obtaining oscillatory modes of particle motion has been studied. It was found that for oscillations of particles with an energy of tens of kiloelectronvolts in the potential well in a well, the field with the amplitude of tens of thousands of Oersteds is required. For the solenoid magnetic field of the solenoid, the formation of electron beam with an energy of 55 keV in the longitudinal and radial directions during its transportation is studied. A section of a magnetron gun was used as the physical object. One possible direction is to combine the two matched magnetic systems of the gun to create the potential magnetic field well. It is shown that, for the chosen conditions, the motion of electrons can be associated with the model of three-dimensional oscillations. In this work, on the basis of the Hamiltonian formalism of the motion of electrons in a magnetic field and an algorithm for numerically finding solutions to the differential equations of dynamics, a software tool is constructed that allows one to obtain arrays of values of particle trajectories in the volume. The use of the software made it possible to simulate the main dependences of the motion of the electron beam in a given two-mode solenoid magnetic field. The results of numerical simulation of electron trajectories in the gradient magnetic field with the point secondary emission cathode located in the middle of the system are presented. The formation of the beam with energy of 55 keV in the radial and longitudinal directions during its transportation in a solenoid magnetic field with a large gradient is considered. For significant time intervals, the possibility of three-dimensional oscillations is shown and the operating modes of the magnetic system are obtained, in which the particle undergoes stable three-dimensional oscillations. The influence of the initial conditions during emission on the occurrence of the reciprocating oscillatory effect has been studied. It is shown that for a given electron energy and fixed magnetic field, the parameter that determines the reflection of a particle, is the polar angle of entry relative to the axis of the cylindrical magnetic field. The dependence of the formation of the final distribution of particles on the amplitude and gradient of the magnetic field along the axis of the system is investigated. The results of numerical simulation on the motion of the electron flow are presented. The characteristics of the resulting electron beam are considered on the basis of a model of electron flow motion. The obtained simulation results show that it is possible to establish the phenomenon of oscillatory-return longitudinal motion under experimental conditions.
 Keywords: electron beam, magnetron gun, three-dimensional oscillations, electron dynamics, gradient magnetic field, mathematical modeling.

Confinement in spherical and cylindrical toroids: A—Electrons in quantum dots B—Electromagnetic multipole sources and fields

This contribution is motivated by the current interest in topological materials and the studies in toroidal dipole interactions in metamaterials and nanophotonics. Its contents are presented in two parts, one on reviews of electrons in cylindrical boxes and magnetic fields and of electromagnetic multipole sources and fields in spherical toroids and new results on a complete family of electromagnetic multipole sources and fields in cylindrical toroids. The discussion and outlook of both parts may be helpful to appreciate the progress since previous reviews and also current works under way.

МОДЕЛЮВАННЯ КОЛИВАЛЬНИХ І ПОВОРОТНИХ ТРАЄКТОРІЙ ЕЛЕКТРОНІВ В ГРАДІЄНТНОМУ МАГНІТНОМУ ПОЛІ МАГНЕТРОННОЇ ГАРМАТИ

Розглянуто рух електронів в циліндричному магнітному полі зі змінною напруженістю вздовж осі поля. Використано математичні та чисельні моделі перетворення експеримегтальних даних аналітичними функціями. З метою отримання прецизійних характеристик вивчено формування пучка з енергією 55 кеВ в повздовжньому і радіальному напрямках при його транспортуванні в магнітному полі соленоїда. Показано, що руху електронів можна зіставити оптичну модель проходження світлових променів в середовищі з градієнтним коефіцієнтом, що залежить від радіуса. Побудовано програмний засіб, використання якого дало можливість промоделювати основні залежності руху електронного пучка в заданому соленоїдальному магнітному полі. Представлено результати чисельного моделювання траєкторій електронів в градієнтному магнітному полі магнетронній гармати з вторінноемісійним катодом. Розглянуто формування пучка з енергією 55 кеВ в радіальному і поздовжньому напрямках при його транспортуванні в соленоїдальному магнітному полі з великим градієнтом. Отримано режими роботи гармати, при яких частка відчуває ефект "пляшкового горлечка" і завершує свій рух поверненням в прикатодну область. Таким чином, отримані біфуркаційні режими динаміки часток при їх русі вздовж осі транспортування як вперед на мішень, так і назад в прикатодну область. Вивчено вплив початкових умов при емісії на виникнення зворотного ефекту. Показано, що при заданій енергії електрона і фіксованому магнітному полі параметром, що визначає відображення частки, є полярний кут вльоту щодо осі циліндричного магнітного поля. Досліджено залежність формування підсумкового розподілу від амплітуди і градієнта магнітного поля вздовж осі системи. Наводяться результати чисельного моделювання по руху трубчастого електронного потоку. Вивчено можливість управління поздовжньої координати точки повернення електрона. На основі моделі руху електронного потоку розглянуті характеристики результуючого електронного пучка.

Design of Highly Uniform Three Dimensional Spherical Magnetic Field Coils for Atomic Sensors

In this paper, three dimensional spherical magnetic field coils are proposed and optimized for atomic sensors that require highly uniform magnetic field coils within a limited volume. The design objective of the uniform coil is transformed into a nonlinear optimization model with constraints, which is solved by combining with the particle swarm optimization algorithm. Compared with the traditional cylindrical tri-axial magnetic field coil system whose volume is limited by the aspect ratio of the coil structure, the three dimensional spherical coils not only effectively reduce the volume but also provide consistent magnetic field performance in the three coordinate axis directions. It is of great significance to the miniaturization of atomic sensors. The theoretical calculation shows that the uniformity of spherical coil is improved by about 2 to 3 orders of magnitude compared with the Lee-Whiting coil and the saddle coil. The measurements show that the magnetic field uniformity of our design reached $1.5\times 10^{-4}$ along the ${z}$ -axis within a range of $\pm 0.25{R}$ . The actual magnetic field distribution is basically consistent with the theory. However, due to the limited processing and experimental conditions, the actual magnetic field uniformity is 1 to 2 orders of magnitude lower than the theory.

Beam and Sector Modes of Electron Fluxes in Cylindrical Magnetic Field of Magnetron Gun

Beam and Sector Modes of Electron Fluxes in Cylindrical Magnetic Field of Magnetron Gun

Numerical-field evaluation of an efficiency of a shortening of a three-phase stator winding of a cylindrical magnetic field inductor

The article proposes the implementation of the on-board battery system of energy accumulation of the DC rail - a reinforcing point that provides regulated parameters for the quality of electrical energy in the contact network. The expediency of using a matching converter, which provides the principle of separate commutation, in order to minimize the loss of switching of the power keys of the converter, is shown. The location of the reinforcement point in the immediate vicinity of the consumer - directly on the rolling stock - on a locomotive or in a special trailer car is substantiated. The energy and mass parameters of the system are estimated. The calculations are made to make the choice of specific power keys of the converter. The optimal frequency of switching of the power keys of the converter is determined, which provides a compromise between the overall properties of the magnetic elements and the losses in the magnetic material. The necessary value of transformer scattering inductance, mass of magnetic elements and batteries is estimated.

Numerical-field evaluation of an efficiency of a shortening of a three-phase stator winding of a cylindrical magnetic field inductor

The efficiency of cylindrical magnetic field inductors is determined by the value of the field inside their working chamber. This field is driven by a three-phase stator winding. The electrical quantities and magnetic induction in the inductor depend on its shortening. The purpose of this work is to determine the rational shortening of the stator winding. The solution of the problem is achieved on the basis of numerical calculations of magnetic fields in the FEMM software package using the finite element method. The construction of physical and geometric design models of the stator, calculations of magnetic fields and electromagnetic parameters of the inductor are automated using the created Lua script built into the FEMM program. The pictures of the distribution of magnetic field lines with diametric and shortened stator windings are given. A comparison is made between the EMF and the winding voltage, as well as the distribution of the magnetic induction over the surface of the working chamber and along the center line of the teeth with different variants of shortening the winding pitch.

Unraveling the Internal Magnetic Field Structure of the Earth-directed Interplanetary Coronal Mass Ejections During 1995 – 2015

The magnetic field configurations associated with interplanetary coronal mass ejections (ICMEs) are the in situ manifestations of the entrained magnetic structure associated with coronal mass ejections (CMEs). We present a comprehensive study of the internal magnetic field configurations of ICMEs observed at 1 AU by the Wind mission during 1995 – 2015. The goal is to unravel the internal magnetic structure associated with the ICMEs and establish the signatures that validate a flux-rope structure. We examine the expected magnetic field signatures by simulating spacecraft trajectories within a simple flux rope, i.e., with circular–cylindrical (CC) helical magnetic field geometry. By comparing the synthetic configurations with the 353 ICME in situ observations, we find that only 152 events ( $F_{r}$ ) display the clear signatures of an expected axial-symmetric flux rope. Two more populations exhibit possible signatures of flux rope; 58 cases ( $F^{-}$ ) display a small rotation ( ${<}\,90^{\circ}$ ) of the magnetic field direction, interpreted as a large separation of the spacecraft from the center, and, 62 cases ( $F^{+}$ ) exhibit larger rotations, possibly arising from more complex configuration. The categories, $C_{x}$ (14%) and $E$ events (9%), reveal signatures of complexity possibly related with evolutionary processes. We then reconstruct the flux ropes assuming CC geometry. We examine the orientation and geometrical properties during the solar activity levels at the end of Solar Cycle 22 (SC22), SC23 and part of SC24. The orientation exhibits solar cycle trends and follow the heliospheric current sheet orientation. We confirm previous studies that found a Hale cycle dependence of the poloidal field reversal. By comparing our results with the occurrence of CMEs with large angular width ( $\mbox{AW}>60^{\circ}$ ) we find a broad correlation suggesting that such events are highly inclined CMEs. The solar cycle distribution of bipolar vs. unipolar $B_{z}$ configuration confirms that the CMEs may remove solar cycle magnetic field and helicity.

Near-singular equilibrium currents near magnetic islands with broken symmetry

The conventional cylindrical analytical model of a magnetic island is symmetric with respect to combined reflection in the poloidal and toroidal angles, a symmetry property sometimes called ‘stellarator symmetry’. There are cancellations in the pressure driven currents when an island is stellarator symmetric that are not there when the symmetry is broken. When the symmetry is broken, new aspects of the island physics emerge. The diamagnetic current driven by the scalar pressure is no longer ambipolar. The pressure-driven current generally has a logarithmic (integrable) singularity at the island separatrix. These effects manifest themselves when taking into account incomplete flattening of the pressure along magnetic field lines. A small magnetic island has only a small effect on the ambient pressure gradient, so that the pressure is not constant on the flux surfaces near the island. For larger islands, this behavior persists near the X-lines. The equilibrium solutions with a small island are to be compared with three-dimensional magnetohydrodynamic equilibrium solutions that are constrained to have simply nested flux surfaces, where the pressure-driven current goes like 1/x near rational surfaces, where x is the distance from the rational surface. This paper presents an investigation of the pressure driven current near a small magnetic island in a cylindrical magnetic field with perturbed circular flux surfaces. The conventional analytical cylindrical model of a field with a magnetic island is augmented with a resonant component that breaks the stellarator symmetry without breaking the flux surfaces. The effects of stellarator symmetry on magnetic islands in tokamaks are of particular interest in the context of the stabilization of edge localized modes by resonant magnetic perturbations. In stellarators, the design studies for the major contemporary devices have discarded half the design parameters available for optimization at the outset by assuming stellarator symmetry.