Tangential Field Research Articles

ON RULED SURFACES CONSTRUCTED BY THE EVOLUTION OF A POLYNOMIAL SPACE CURVE

In this paper, we present the evolutions of the ruled surfaces constructed by the tangent, normal-like, and binormal-like vector fields of a polynomial space curve. These evolutions of the ruled surfaces depend on the evolutions of their directrices using the Flc (Frenet like curve) frame along a polynomial space curve. Therefore, the evolutions of a polynomial curve are expressed in the first step of this study. Then, some geometric properties of the special ruled surfaces are investigated and examples of these surfaces are given and their graphics are drawn using the Mathematica 9 program.

An analytical solution of the rope-sheave contact in static conditions based on a bristle model

This paper presents an analytical solution for the rope-sheave contact problem in static conditions, also applicable to belt-pulley problems and similar mechanisms. The rope is assumed under constant and unequal loads at the two ends, as in an elevator when the brake is acting on the drive sheave and the weights of the cabin and counterweights are different. The rope is assumed to behave as a rod without bending stiffness. Assuming a bristle model for the rope-sheave contact and Coulomb friction, the balance of forces in a differential slice of the rope is used to obtain a closed-form solution for the axial force field and the normal and tangential contact force fields. This analytical solution is found first in the case of a bristle model with tangential flexibility but axially rigid. Then, the model is extended to axially flexible bristles, that allows the rope to sheave relative penetration. The solution is valid until one cross-section of the rope achieves the saturated tangential friction force. The value of the axial load when this condition is met is identified. If the high-load further increases, the rope in contact with the sheave is separated in two areas, the area next to the low-load remains fully stuck to the sheave while the area next to the high-load shows exactly the saturated friction force. This paper calculates the angle of separation between the two areas and the axial force field and normal and tangential contact force fields, being all these functions piece-wisely defined. Finally, the paper presents numerical results for a particular example of all the analytical solutions.

Effect of mass and heat transfer on EHD stability of two dusty liquid layers between two inclined rigid plates

The electrohydrodynamics (EHD) instability of two separate overlapping viscous particle fluids moving in a porous medium is the subject of this paper. The incompressible packaging contains microscopic, uniformly sized fine dust particles. The system is influenced by a tangential electric field that remains constant. The abbreviated formulation of Hsieh is employed to account for the impact of mass and heat transfer (MHT). The problem solution follows the viscous potential theory (VPT) because of the problem complexity in mathematics. The significance of fluid-particle mixing in several applications of practical physics and engineering operates as the guiding force behind this investigation. The standard normal modes methodology is used to examine the standard fundamental equations of motion. The essential mechanisms of the nonlinear technique are the formulations of the linear controlling fundamental formulae and the application of the appropriate nonlinear boundary criteria. A number of nondimensional characteristic parameters are produced by the technique. The nonlinear stability results in a nonlinear Landau–Ginzburg equation. By giving the physical parameter numerical values, the stability designs have been graphically represented. Therefore, both linear and nonlinear approaches are depicted to illustrate the impacts of different physical quantities. Using the homotopy perturbation approach and the idea of extended frequency, a uniform approximate solution for a nonlinear interface displacement is provided. He’s frequency approach yields another nonperturbative solution of the surface displacement solution, which is validated using the Runge–Kutta method.

On the nonlinear behaviour of the Rayleigh–Taylor instability with a tangential electric field for inviscid and perfect dielectric fluids

Fluid interfacial instability induced by gravity or external acceleration, known as the Rayleigh–Taylor instability, plays an important role in both scientific research and industrial application. How to control this instability is challenging. Researchers have been actively exploring the suppression method of applying electric fields parallel to dielectric fluid interfaces. The instability is characterized by the penetration of fingers at the interface. The velocities at the finger tips are the most important quantities since they characterize how fast the penetration occurs. The dynamics of the fingers is nonlinear. We present a nonlinear perturbation procedure for determining the amplitude and velocity of fingers at a Rayleigh–Taylor unstable interface between two incompressible, inviscid, immiscible and perfectly dielectric fluids in the presence of a horizontal electric field in two dimensions. The analytic formulas are displayed explicitly up to the third order of the initial disturbance. The comparison with the data from numerical simulations based on the vortex sheet method shows the theoretical formulas can capture well the nonlinear behaviour of the fingers. It is known that the interplay between the electric field and the fluids can lead to the suppression of interfacial instability. We further analyse the electrical force along the interface and show how this force leads to the instability suppression in our setting. It has been reported numerically in the literature that switching the electric permittivities of the fluids leads to quantitative differences in finger velocity. We show theoretically this phenomenon can only be explained by the nonlinear behaviour of the system.

Heat transfer and hydromagnetic electroosmotic Von Kármán swirling flow from a rotating porous disc to a permeable medium with viscous heating and Joule dissipation

AbstractMagnetohydrodynamic flow and heat transfer in an ionic viscous fluid in a porous medium induced by a stretching spinning disc and modulated by electroosmosis under an axial magnetic field and radial electrical field is presented in this study. The effects of convective wall boundary conditions, Joule heating and viscous dissipation are incorporated. The governing partial differential conservation equations are transformed into a system of self‐similar coupled, nonlinear ordinary differential equations with associated boundary conditions. The Matlab bvp4c solver featuring a shooting technique and the fourth‐order Runge–Kutta–Fehlberg method are used to numerically solve the governing dimensionless boundary value problem. Multivariate analysis is also performed to examine the thermal characteristics. An increase in rotation parameter induces a reduction in the radial velocity, whereas it elevates the tangential velocity. Greater electrical field parameter strongly damps the radial velocity whereas it slightly decreases the tangential velocity. Increasing magnetic parameter also damps both the radial and tangential velocities. An increment in electroosmotic parameter substantially decelerates the radial flow but has a weak effect on the tangential velocity field. Increasing permeability parameter (inversely proportional to permeability) markedly damps both radial and tangential velocities. The pressure gradient is initially enhanced near the disk surface but reduced further from the disk surface with increasing magnetic parameter and electrical field parameter, whereas the opposite effect is produced with increasing Joule dissipation. Increasing magnetic and rotational parameters generate a strong heating effect and boost temperature and thermal boundary layer thickness. Nusselt number is boosted with increasing Brinkman number (viscous heating effect) and Reynolds number. The simulations are relevant to electromagnetic coating flows, bioreactors and electrochemical sensing technologies in medicine.

Longitudinal wall shear stress evaluation using centerline projection approach in the numerical simulations of the patient-based carotid artery

In this numerical study, areas of the carotid bifurcation and of a distal stenosis in the internal carotid artery are closely observed to evaluate the patient’s current risks of ischemic stroke. An indicator for the vessel wall defects is the stress exerted by blood on the vessel tissue, typically expressed by the amplitude of the wall shear stress vector (WSS) and its oscillatory shear index. To detect negative shear stresses corresponding with reversal flow, we perform orientation-based shear evaluation. We investigate the longitudinal component of the wall shear vector, where tangential vectors aligned longitudinally with the vessel are necessary. However, resulting from imaging segmentation resolution of patients’ computed tomography angiography scans and stenotic regions, the geometry model’s mesh is non-smooth on its surface areas and the automatically generated tangential vector field is discontinuous and multi-directional, making an interpretation of our orientation-based risk indicators unreliable. We improve the evaluation of longitudinal shear stress by applying the projection of the vessel’s centerline to the surface to construct smooth tangential field aligned longitudinally with the vessel. We validate our approach for the longitudinal WSS component and the corresponding oscillatory index by comparing them to results obtained using automatically generated tangents in both rigid and elastic vessel modeling and to amplitude-based indicators. We present the major benefit of our longitudinal WSS evaluation based on its directionality for the cardiovascular risk assessment, which is the detection of negative WSS indicating persistent reversal or transverse flow. This is impossible in the case of the amplitude-based WSS.

All Acoustical Excitation of Spin Waves in High Overtone Bulk Acoustic Resonator

The hybrid high overtone bulk acoustic wave resonators (HBARs) consisting of a piezoelectric film transducers and gallium gadolinium garnet substrates with yttrium iron garnet films (YIG-GGG-YIG) are used for experimental excitation and detection of acoustically driven spin waves (ADSWs). Two types of HBAR transducers made of Al-ZnO-Al films (differed through the electrodes’ geometry) were deposited onto YIG-GGG-YIG trilayers with different YIG film thicknesses and doping levels and served for excitation of multimode HBAR at gigahertz frequencies. ADSWs were detected by measuring the shifts of resonant HBAR modes in a tangential external magnetic field when the conditions for magnetoelastic resonance (MER) were satisfied. It was shown that the design of the transducer with a continuous bottom electrode provides all acoustical excitation of spin waves (pure ADSWs), suppressing the additional inductive magnetic dynamics excitation due to the electrodes’ geometry. The theoretical study of the HBAR spectrum in a magnetic field showed that the resonance harmonics in the MER region can either almost continuously transfer from one to another, or decay and form an evident magnetoelastic gap. In this case, the shift of resonant frequencies can achieve several intermodal distances. The results obtained are important for applications of HBAR-based devices in spintronics and magnonics.

Erratum to “Navier–Stokes equations in a curved thin domain, Part III: thin-film limit”

There are two flaws in the third part [3] of our study on the Navier--Stokes equations in a curved thin domain. The first one is that the form of Ladyzhenskaya's inequality on a closed surface taken from the arXiv version [2] of the second part of our study is incorrect. The second one is that a wrong claim is used in the proofs of lemmas in [3, Section 6.3] which give estimates for the weighed potential part of a tangential surface vector field. This erratum corrects these flaws.

Abstract GS5-12: Hypofractionated Radiotherapy in patients with Breast Cancer (HRBC): Acute toxicity data of a phase III randomized study

Abstract Background HRBC is a phase III randomized open label study of adjuvant radiotherapy in patients with breast cancer. In this study we compared a 3 weeks radiation schedule with 2 weeks. Materials and methods Patients with breast cancer, stage I-III, post mastectomy or after breast conservative surgery who needed adjuvant locoregional radiotherapy were randomized to 34Gy in 10 fractions over 2 weeks (study arm) or 35Gy in 15 fractions over 3 weeks to the chest wall and 40Gy/15#/3wks to breast and supraclavicular fossa (control arm). Boost dose when indicated was 8Gy/2# in both the arms. Patients were planned on simulator with 2 tangential fields to breast/chest wall and incident supraclavicular fossa field. Acute toxicity was assessed using a RTOG grading system. Assessment was carried out weekly during radiotherapy and at 4 weeks after treatment by the physician. Cosmetic outcome was assessed using Harvard/NSABP/RTOG scale. The toxicity between the two arms was compared using Fisher’s exact test. The trial was approved by institutional ethics committee. This trial is registered with ClinicalTrials.gov, number NCT04075058. Results This study included 1121 patients. Median follow up was 35 months (range 6-84 months). Mean age was 48 year (range 24-80 years). The patient characteristics were comparable between the two arms except for more mastectomies in the 3 week arm and more node positive patients in the 2 week arm. There were more oestrogen receptor positive tumors in the 3 week arm. Acute skin toxicities were comparable between the two arms. Grade 2 and 3 skin toxicity was 98(17%) and 82(15%); and 16(3%) and 10(2%) in the 3 week and 2 week arm (p=0.15), respectively. Cosmetic outcome was significantly better in 2 week arm 94% as compared to 90% in the 3 week arm (p=0.016). Conclusion The two radiation schedules were comparable in terms of acute skin toxicity. Cosmetic outcome was better in the 2 week schedule. Citation Format: Budhi Singh Yadav, Divya Dahiya, Manish Gupta. Hypofractionated Radiotherapy in patients with Breast Cancer (HRBC): Acute toxicity data of a phase III randomized study [abstract]. In: Proceedings of the 2022 San Antonio Breast Cancer Symposium; 2022 Dec 6-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2023;83(5 Suppl):Abstract nr GS5-12.

Abstract P1-10-14: Higher radiation dose to the heart in left sided breast cancer; anatomy versus dosimetry

Abstract Abstract: Background: There is assumption that omitting the internal mammary chain radiotherapy (IMC RT) in patients with breast cancer (BC) will significantly reduce the cardiac exposure for all patients regardless the cardiac anatomy of each patient. Aim: to evaluate the impact of IMC RT on the dose received by the heart and its chambers in patients with favorable versus unfavorable cardiac anatomy. Patients and methods: CT scans were obtained of 20 patients with left-sided BC, 10 with favorable and 10 with unfavorable cardiac anatomy. Three plans were generated for each patient, one treating only the breast with tangents, and one treating the breast and IMC with wide photon tangents, and one treating the breast and IMC to 50Gy with photon tangent fields and a matching medial electron field. Dose volume histograms (DVHs) were generated for the heart and chambers. The equivalent uniform doses (EUDs) were calculated for each DVH, and the mean EUDs for plans with unfavorable and favorable cardiac anatomy were compared using a two-sided two-sample T-test Results: The mean dose received by the heart from plans with tangents plus IMC fields in patients with favorable cardiac anatomy was significantly lower than that received from plans with tangents only or wide tangents in patients with unfavorable anatomy (P < .0001). The average EUD for plans with tangents and IMC fields in the favorable group was 16 Gy (SD = 4.5) as compared to 36 Gy (SD = 3.6) and 37 Gy (SD = 5.1) for plans with tangents only and wide tangents in the unfavorable group, respectively ((P < .0001). The doses to the right ventricle were not significantly different. Conclusions: Ttreatment plans should be individualized based on the cardiac anatomy of each patient. Citation Format: Mohamed Alm El-Din, Andrzej Niemierko, Alphonse Taghian. Higher radiation dose to the heart in left sided breast cancer; anatomy versus dosimetry [abstract]. In: Proceedings of the 2022 San Antonio Breast Cancer Symposium; 2022 Dec 6-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2023;83(5 Suppl):Abstract nr P1-10-14.

Low doses to the heart in daily practice for treating left-sided breast cancer using accelerated partial-breast irradiation by multicatheter brachytherapy and deep-inspiration breath-hold using a SIB

PurposeThe aim of this study was to analyze the heart dose for left-sided breast cancer that can be achieved during daily practice in patients treated with multicatheter brachytherapy (MCBT) accelerated partial-breast irradiation (APBI) and deep-inspiration breath-hold (DIBH) whole-breast irradiation (WBI) using a simultaneous integrated tumor bed boost (SIB)—two different concepts which nonetheless share some patient overlap.Materials and methodsWe analyzed the nominal average dose (Dmean) to the heart as well as the biologically effective dose (BED) and the equivalent dose in 2‑Gy fractions (EQD2) for an α/β of 3 in 30 MCBT-APBI patients and 22 patients treated with DIBH plus SIB. For further dosimetric comparison, we contoured the breast planning target volume (PTV) in each of the brachytherapy planning CTs according to the ESTRO guidelines and computed tangential field plans. Mean dose (Dmean), EQD2 Dmean, and BED Dmean for three dosing schemes were calculated: 50 Gy/25 fractions and two hypofractionated regimens, i.e., 40.05 Gy/15 fractions and 26 Gy/5 fractions. Furthermore, we calculated tangential field plans without a boost for the 22 cases treated with SIB with the standard dosing scheme of 40.05 Gy/15 fractions.ResultsMCBT and DIBH radiation therapy both show low-dose exposure of the heart. As expected, hypofractionation leads to sparing of the heart dose. Although MCBT plans were not optimized regarding dose to the heart, Dmean differed significantly between MCBT and DIBH (1.28 Gy vs. 1.91 Gy, p < 0.001) in favor of MCBT, even if the Dmean in each group was very low. In MCBT radiation, the PTV–heart distance is significantly associated with the dose to the heart (p < 0.001), but it is not in DIBH radiotherapy using SIB.ConclusionIn daily practice, both DIBH radiation therapy as well as MCBT show a very low heart exposure and may thus reduce long term cardiac morbidity as compared to currently available long-term clinical data of patients treated with conventional tangential field plans in free breathing. Our analysis confirms particularly good cardiac sparing with MCBT-APBI, so that this technique should be offered to patients with left-sided breast cancer if the tumor-associated eligibility criteria are fulfilled.

Are Radiation Target Volumes for Postmastectomy Radiation Therapy Too Large? Initial Report of the Complication Avoidance of Reconstruction Implant Radiation Therapy (CARIT) Study.

Following mastectomy for breast cancer, women may choose implant-based reconstruction for many reasons, such as cosmesis, self-identity, and the ability to wear particular items of clothing. However, postmastectomy radiation therapy (PMRT) can compromise these cosmetic goals, including as much as a 40% loss of implant rate. To minimize the risk of radiation toxicity, it is important to consider how clinical target volumes (CTVs) can be optimized in PMRT to preserve the implant and reduce complications. Typically, guidelines from organizations such as the Radiation Oncology Group are used, which include regions previously encompassed by tangential fields. This includes all structures below the pectoralis muscle, such as the chest wall, where the risk of recurrence is negligible; this technique often requires incidental inclusion of portions of the lung and heart plus circumferential radiation of the implant. We present the preliminary single institution case series of a technique of complication avoidance of reconstruction implant radiation therapy, called CARIT, where the chest wall, and a large proportion of the implant, is not irradiated. In a retrospective review of 30 cases in which CARIT has been attempted, it was found that 24% of patients treated required a second surgery due to Baker grade III/IV capsular contracture. Using the Modified Harvard Harris Cosmetic Scale, 66.5% of patients had cosmetic outcomes rated as "good" or "excellent". CARIT could offer a technique to reduce complications in postmastectomy implant-based reconstruction patients, with our next steps focusing on improving dosimetry, and formally comparing the cosmesis and tumor control aspects with commonly used techniques.

Collapsed Cone Superposition Algorithm Validation for Chest Wall Tangential Fields using Virtual Wedge Filters.

Virtual wedge (VW) is used in radiotherapy to compensate for missing tissues and create a uniform dose distribution in tissues. According to TECDOC-1583 and technical reports series no. 430, evaluating the dose calculation accuracy is essential for the quality assurance of treatment planning systems (TPSs). In this study, the dose calculation accuracy of the collapsed cone superposition (CCS) algorithm in the postmastectomy radiotherapy of the chest wall for breast cancer was evaluated by comparing the calculated and measured dose in VW fields. Two tangential fields with the typical VW angles were planned using ISOgray TPS in a thorax phantom. The CCS algorithm was used for dose calculation at 6 and 15 MV photon beams. The obtained dose distributions from EBT3 film spaces and TPS were evaluated using the gamma index. The measured and calculated dose values using VW in a heterogeneous medium with different beam energies were in a good agreement with each other (acceptance rate: 88.0%-93.4%). The calculated and measured data did not differ significantly with an increase/decrease in wedge angle. In addition, the results demonstrated that ISOgray overestimated and underestimated the dose of the soft tissue and lung in the planned volume, respectively. According to the results of gamma index analysis, the calculated dose distribution using VW model with the CCS algorithm in a heterogeneous environment was within acceptable limits.

On Surface Resistivity Measurements of Thin Insulation Materials

Surface resistivity measurements are frequently used for material characterization. However, the influence of sample thickness is not covered sufficiently in ASTM D257 and IEC 62631-3-2 standards. In this work, electric field simulations and polarization–depolarization current (PDC) measurements are used to study the thickness dependence of such measurements. It is found that measurements according to the standards are not reasonable for low thickness (<1 mm) and high surface resistivity (>1013– <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{{14}}~ {\Omega } $ </tex-math></inline-formula> ). The dependence on thickness is shown to be mainly due to the different tangential electric field stress along the measured surface. Furthermore, indications for charge injection at high electric field stress inside the sample volume are found by a positive polarity of the depolarization currents. A novel electrode configuration for more accurate (more than one order of magnitude) and much less thickness-dependent surface resistivity measurements is proposed in this work and its benefits are demonstrated. It is also shown how the parasitic influence of an electrode holder can be effectively reduced by more than one order of magnitude when measuring surface resistivities. In addition, it is found that polarization times for steady-state surface resistivity values should be at least several minutes instead of the suggested 60 s from standards.

JCMT BISTRO Observations: Magnetic Field Morphology of Bubbles Associated with NGC 6334

We study the Hii regions associated with the NGC 6334 molecular cloud observed in the submillimeter and taken as part of the B-fields In STar-forming Region Observations Survey. In particular, we investigate the polarization patterns and magnetic field morphologies associated with these Hii regions. Through polarization pattern and pressure calculation analyses, several of these bubbles indicate that the gas and magnetic field lines have been pushed away from the bubble, toward an almost tangential (to the bubble) magnetic field morphology. In the densest part of NGC 6334, where the magnetic field morphology is similar to an hourglass, the polarization observations do not exhibit observable impact from Hii regions. We detect two nested radial polarization patterns in a bubble to the south of NGC 6334 that correspond to the previously observed bipolar structure in this bubble. Finally, using the results of this study, we present steps (incorporating computer vision; circular Hough transform) that can be used in future studies to identify bubbles that have physically impacted magnetic field lines.

Abnormal Signals Elimination in Hardness Evaluation Using Barkhausen Noise and Tangential Magnetic Field

Abnormal Signals Elimination in Hardness Evaluation Using Barkhausen Noise and Tangential Magnetic Field

Surface instability of static liquid metal in magnetized fusion plasma

Understanding surface instability in magnetized fusion plasma supports the appropriate implementation and handling of liquid metal as plasma facing components (PFCs) in future fusion reactors. A Lagrange equation describing a viscous liquid surface deformation in a magnetized plasma is derived using Rayleigh’s method. Its solution justifies the general instability criterion and helps in characterizing the key interactions driving such instability under fusion conditions. Surface tension and gravity, especially with the poloidal angles of the lower part of a plasma chamber, mainly stabilize the liquid surface at small and large disturbance wavelengths, respectively. The sheath electric field and the external tangential magnetic field cause the liquid surface to disintegrate at an intermediate wavelength. Practically, a magnetic confinement fusion (MCF) device requires a strong magnetic field for confinement. The study suggests that such a strong field dominates the rest and governs instability. In addition, this implies that the configuration of a static planar free liquid surface is difficult to adopt as a candidate for handling the liquid metal as PFCs in next step MCF devices.

Magnetic potential based formulation for linear and non-linear 3D RF sheath simulation

This paper reports a new numerical scheme to simulate the radio-frequency (RF) induced RF sheath, which is suitable for a large 3D simulation. In the RF sheath boundary model, the tangential component of the electric field () is given by the gradient of a scalar electric field potential. We introduce two additional scalar potentials for the tangential components of the magnetic field, which effectively impose the normal electric displacement (D n ) on the plasma sheath boundary condition via in-homogeneous Neumann boundary condition and constrain the tangential electric field on the surface as curl-free (). In our approach, the non-linear sheath impedance is formulated as a natural extension of the large thickness (or asymptotic) sheath limit (), allowing for handling both asymptotic and non-linear regimes seamlessly. The new scheme is implemented using the Petra-M finite element method analysis framework and is verified with simulations in the literature. The significance of non-linearity is discussed in various plasma conditions. An application of this scheme to asymptotic RF sheath simulation on the WEST ICRF antenna side limiters is also discussed.

Electrostatic force on a spherical particle confined between two planar surfaces.

A charge-free particle in a uniform electric field experiences no net force in an unbounded domain. A boundary, however, breaks the symmetry and the particle can be attracted or repelled to it, depending on the applied field direction [Z. Wang et al., Phys. Rev. E, 2022, 106, 034607]. Here, we investigate the effect of a second boundary because of its common occurrence in practical applications. We consider a spherical particle suspended between two parallel walls and subjected to a uniform electric field, applied in a direction either normal or tangential to the surfaces. All media are modeled as leaky dielectrics, thus allowing for the accumulation of free charge at interfaces, while bulk media remain charge-free. The Laplace equation for the electric potential is solved using a multipole expansion and the boundaries are accounted for by a set of images. The results show that in the case of a normal electric field, which corresponds to a particle between two electrodes, the force is always attractive to the nearer boundary and, in general, weaker that the case of only one wall. Intriguingly, for a given particle-wall separation we find that the force may vary nonmonotonically with confinement and its magnitude may exceed the one-wall value. In the case of tangential electric field, which corresponds to a particle between insulating boundaries, the force follows the same trends but it is always repulsive.

Waveguide Analysis of Radiofrequency Transmission in Well Tubulars for Electromagnetic Heating of Heavy Oil

This paper presents the numerical modelling and simulation of a 2D vertical well tubular model excited by a coaxial radiofrequency transmission line placed in its annular space for the purpose of downhole RF energy transmission. The study identifies the mechanism of energy losses due to coupling between the transmission line and steel tubing and casing using resonance mode analysis. The design of a left-handed artificial power line is proposed to minimize the losses due to the right-handed properties of the coaxial transmission line. The design utilizes ideal lumped element method to determine the left-handedness of the right-handed coaxial transmission line over the industrial heating radio-frequency band. The model is developed and simulated using COMSOL multi-physics commercial simulation software. The effect of transmission line position within the annular space on the tangential magnetic field and resulting power losses along the tubing is discussed. It is observed that the resulting artificial power line improves RF power transmission over 60 m depths of the vertical oil well within the industrial heating radiofrequency band.