Currently,three types of superconducting quadrupole magnets are used in particle accelerators:cos 2θ,CCT,and serpentine.However,all three coil configurations have complex spatial geometries,which make magnet manufact...Currently,three types of superconducting quadrupole magnets are used in particle accelerators:cos 2θ,CCT,and serpentine.However,all three coil configurations have complex spatial geometries,which make magnet manufacturing and strain-sensitive superconductor applications difficult.Compared with the three existing quadrupole coils,the racetrack quadrupole coil has a simple shape and manufacturing process,but there have been few theoretical studies.In this paper,the two-dimensional and three-dimensional analytical expressions for the magnetic field in coil-dominated racetrack superconducting quadrupole magnets are presented.The analytical expressions of the field harmonics and gradient are fully resolved and depend only on the geometric parameters of the coil and current density.Then,a genetic algorithm is applied to obtain a solution for the coil geometry parameters with field harmonics on the order of 10^(-4).Finally,considering the practical engineering needs of the accelerator interaction region,electromagnetic design examples of racetrack quadrupole magnets with high gradients,large apertures,and small apertures are described,and the application prospects of racetrack quadrupole coils are analyzed.展开更多
For a practical superconducting quantum interference device(SQUID) based measurement system,the Tesla/volt coefficient must be accurately calibrated.In this paper,we propose a highly efficient method of calibrating ...For a practical superconducting quantum interference device(SQUID) based measurement system,the Tesla/volt coefficient must be accurately calibrated.In this paper,we propose a highly efficient method of calibrating a SQUID magnetometer system using three orthogonal Helmholtz coils.The Tesla/volt coefficient is regarded as the magnitude of a vector pointing to the normal direction of the pickup coil.By applying magnetic fields through a three-dimensional Helmholtz coil,the Tesla/volt coefficient can be directly calculated from magnetometer responses to the three orthogonally applied magnetic fields.Calibration with alternating current(AC) field is normally used for better signal-to-noise ratio in noisy urban environments and the results are compared with the direct current(DC) calibration to avoid possible effects due to eddy current.In our experiment,a calibration relative error of about 6.89 × 10-4is obtained,and the error is mainly caused by the non-orthogonality of three axes of the Helmholtz coils.The method does not need precise alignment of the magnetometer inside the Helmholtz coil.It can be used for the multichannel magnetometer system calibration effectively and accurately.展开更多
The resonant magnetic perturbation(RMP)system is a powerful auxiliary system on tokamaks.On the J-TEXT tokamak,a set of new in-vessel coils is designed to enhance the amplitude of the RMP.The new coils are designed to...The resonant magnetic perturbation(RMP)system is a powerful auxiliary system on tokamaks.On the J-TEXT tokamak,a set of new in-vessel coils is designed to enhance the amplitude of the RMP.The new coils are designed to be two-turn saddle coils.These two-turn saddle coils have been optimized in terms of their structure,support,and protection components to overcome the limitations of the narrow in-vessel space,resulting in a compact coil module that can be accommodated in the vessel.To verify the feasibility of this design,an electromagnetic simulation is performed to investigate the electrical parameters and the generated field of the coils.A multi-field coupled simulation is performed to investigate the capacity of heat dissipation.As a result of these efforts,the new RMP coils have been successfully installed on the J-TEXT tokamak.It has significantly enhanced the RMP amplitude and been widely applied in experiments.展开更多
The relatively fragile low-temperature stability of cryogen-free superconducting magnetic resonance imaging(MRI)magnets requires the careful management of exogenous heat sources.A strongly shielded gradient magnetic f...The relatively fragile low-temperature stability of cryogen-free superconducting magnetic resonance imaging(MRI)magnets requires the careful management of exogenous heat sources.A strongly shielded gradient magnetic field is important for the optimal operation of cryogen-free MRI systems.In this study,we present an enhanced shielding method incorporating a regionalized stray field constraining strategy.By optimizing the constraint parameters,we could develop engineering-feasible gradient coil schemes without increasing system complexity but with the stray field intensity reduced by half.In real measurement in an integrated MRI system,the developed gradient assembly demonstrated good performance and supported to output images of excellent quality.Our findings suggested that the proposed method could potentially form a useful design paradigm for cryogen-free MRI magnets.展开更多
Enhancing plasma uniformity can be achieved by modifying coil and chamber structures in radio frequency inductively coupled plasma(ICP)to meet the demand for large-area and uniformly distributed plasma in industrial m...Enhancing plasma uniformity can be achieved by modifying coil and chamber structures in radio frequency inductively coupled plasma(ICP)to meet the demand for large-area and uniformly distributed plasma in industrial manufacturing.This study utilized a two-dimensional self-consistent fluid model to investigate how different coil configurations and chamber aspect ratios affect the radial uniformity of plasma in radio frequency ICP.The findings indicate that optimizing the radial spacing of the coil enhances plasma uniformity but with a reduction in electron density.Furthermore,optimizing the coil within the ICP reactor,using the interior point method in the Interior Point Optimizer significantly enhances plasma uniformity,elevating it from 56%to 96%within the range of the model sizes.Additionally,when the chamber aspect ratio k changes from 2.8 to 4.7,the plasma distribution changes from a center-high to a saddleshaped distribution.Moreover,the plasma uniformity becomes worse.Finally,adjusting process parameters,such as increasing source power and gas pressure,can enhance plasma uniformity.These findings contribute to optimizing the etching process by improving plasma radial uniformity.展开更多
Research on adaptive deformable mirror technology for voice coil actuators(VCAs)is an important trend in the development of large ground-based telescopes.A voice coil adaptive deformable mirror contains a large number...Research on adaptive deformable mirror technology for voice coil actuators(VCAs)is an important trend in the development of large ground-based telescopes.A voice coil adaptive deformable mirror contains a large number of actuators,and there are problems with structural coupling and large temperature increases in their internal coils.Additionally,parameters of the traditional proportional integral derivative(PID)control cannot be adjusted in real-time to adapt to system changes.These problems can be addressed by introducing fuzzy control methods.A table lookup method is adopted to replace real-time calculations of the regular fuzzy controller during the control process,and a prototype platform has been established to verify the effectiveness and robustness of this process.Experimental tests compare the control performance of traditional and fuzzy proportional integral derivative(Fuzzy-PID)controllers,showing that,in system step response tests,the fuzzy control system reduces rise time by 20.25%,decreases overshoot by 78.24%,and shortens settling time by 67.59%.In disturbance rejection experiments,fuzzy control achieves a 46.09%reduction in the maximum deviation,indicating stronger robustness.The Fuzzy-PID controller,based on table lookup,outperforms the standard controller significantly,showing excellent potential for enhancing the dynamic performance and disturbance rejection capability of the voice coil motor actuator system.展开更多
In global industrialization, efforts have been made to increase the rate of heat transfer in heat exchanger, minimizing the size of heat exchanger to reduce cost as well as increasing the effectiveness. Helical coil h...In global industrialization, efforts have been made to increase the rate of heat transfer in heat exchanger, minimizing the size of heat exchanger to reduce cost as well as increasing the effectiveness. Helical coil heat exchanger (HCHE) has been proven to be effective in improving heat transfer due to its large surface area. In this study, HCHE was designed to provide hot air needed for fluidized bed drying processes. The HCHE design model was fabricated and evaluated to study the efficiency of the hot air output for a laboratory fluidized bed dryer. The mathematical model for estimation of the final (output) temperature of air, Taf, passing through the HCHE was developed and validated experimentally. The drying of bitter kola particulates was carried out with a drying temperature of 50C 3C and a bed height-to-bed diameter ratio (H/D) of 1.5. The time taken to dry bitter kola particulates to 0.4% moisture content was 1 hour 45 minutes. Hence, HCHE is recommended for use in the production of hot for laboratory-scale fluidized bed dryers.展开更多
The development of aqueous Zn batteries is limited by parasitic water reactions,corrosion,and dendrite growth.To address these challenges,an inner Helmholtz plane(IHP)regulation method is proposed by employing low-cos...The development of aqueous Zn batteries is limited by parasitic water reactions,corrosion,and dendrite growth.To address these challenges,an inner Helmholtz plane(IHP)regulation method is proposed by employing low-cost,non-toxic maltitol as the electrolyte additive.The preferential adsorption behavior of maltitol can expel the water from the inner Helmholtz plane,and thus hinder the immediate contact between Zn metal and H_(2)O.Meanwhile,strong interaction between maltitol and H_(2)O molecules can restrain the activity of H_(2)O.Besides,the"IHP adsorption effect"along with the low LUMO energy level of maltitol-CF_(3)SO_(3)^(-)can promote the in-situ formation of an organic-inorganic complex solid electrolyte interface(SEI)layer.As a result,the hydrogen/oxygen evolution side reaction,corrosion,and dendrites issues are effectively suppressed,thereby leading to highly reversible and dendrite-free Zn plating/stripping.The Zn‖I_(2)battery with hybrid electrolytes also demonstrates high electrochemical performance and ultralong cycling stability,showing a capacity retention of 75%over 20000 charge-discharge cycles at a large current density of 5 A g^(-1).In addition,the capacity of the device has almost no obvious decay over20000 cycles even at-30℃.This work offers a successful electrolyte regulation strategy via the IHP adsorption effect to design electrolytes for high-performance rechargeable Zn-ion batteries.展开更多
The methods of improving the dynamic performance of high speed on/off solenoid valve include increasing the magnetic force of armature and the slew rate of coil current, decreasing the mass and stroke of moving parts....The methods of improving the dynamic performance of high speed on/off solenoid valve include increasing the magnetic force of armature and the slew rate of coil current, decreasing the mass and stroke of moving parts. The increase of magnetic force usually leads to the decrease of current slew rate, which could increase the delay time of the dynamic response of solenoid valve. Using a high voltage to drive coil can solve this contradiction, but a high driving voltage can also lead to more cost and a decrease of safety and reliability. In this paper, a new scheme of parallel coils is investigated, in which the single coil of solenoid is replaced by parallel coils with same ampere turns. Based on the mathematic model of high speed solenoid valve, the theoretical formula for the delay time of solenoid valve is deduced. Both the theoretical analysis and the dynamic simulation show that the effect of dividing a single coil into N parallel sub-coils is close to that of driving the single coil with N times of the original driving voltage as far as the delay time of solenoid valve is concerned. A specific test bench is designed to measure the dynamic performance of high speed on/off solenoid valve. The experimental results also prove that both the delay time and switching time of the solenoid valves can be decreased greatly by adopting the parallel coil scheme. This research presents a simple and practical method to improve the dynamic performance of high speed on/off solenoid valve.展开更多
In this paper, an approach to the design of shielded radio-frequency (RF) phased-array coils for magnetic resonance imaging (MRI) is proposed. The target field method is used to find current densities distributed ...In this paper, an approach to the design of shielded radio-frequency (RF) phased-array coils for magnetic resonance imaging (MRI) is proposed. The target field method is used to find current densities distributed on primary and shield coils. The stream function technique is used to discretize current densities and to obtain the winding patterns of the coils. The corresponding highly ill-conditioned integral equation is solved by the Tikhonov regularization with a penalty function related to the minimum curvature. To balance the simplicity and smoothness with the homogeneity of the magnetic field of the coll's winding pattern, the selection of a penalty factor is discussed in detail.展开更多
For a superconducting magnet of magnetic resonance imaging (MRI), the novel approach presented in this paper allows the design of cylindrical gradient and shim coils of finite length. The method is based on identifi...For a superconducting magnet of magnetic resonance imaging (MRI), the novel approach presented in this paper allows the design of cylindrical gradient and shim coils of finite length. The method is based on identification of the weighting of harmonic components in the current distribution that will generate a magnetic field whose z-component follows a chosen spherical harmonic function. Mathematical expressions which relate the harmonic terms in the cylin- drical current distribution to spherical harmonic terms in the field expansion are established. Thus a simple matrix inversion approach can be used to design a shim coil of any order pure harmonic. The expressions providing a spherical harmonic decomposition of the field components produced by a particular cylindrical current distribution are novel. A stream function was applied to obtain the discrete wire distribution on the cylindrical-surface. This method does not require the setting of the target-field points. The discussion referring to matrix equations in terms of condition numbers proves that this novel approach has no ill-conditioned problems. The results also indicate that it can be used to design cylindrical-surface shim coils of finite length that will generate a field variation which follows a particular spherical harmonic over a reasonably large-sized volume.展开更多
基金supported in part by the National Key Research and Development Program of China(No.2022YFA1603402)in part by the National Natural Science Foundation of China(No.11875272)。
文摘Currently,three types of superconducting quadrupole magnets are used in particle accelerators:cos 2θ,CCT,and serpentine.However,all three coil configurations have complex spatial geometries,which make magnet manufacturing and strain-sensitive superconductor applications difficult.Compared with the three existing quadrupole coils,the racetrack quadrupole coil has a simple shape and manufacturing process,but there have been few theoretical studies.In this paper,the two-dimensional and three-dimensional analytical expressions for the magnetic field in coil-dominated racetrack superconducting quadrupole magnets are presented.The analytical expressions of the field harmonics and gradient are fully resolved and depend only on the geometric parameters of the coil and current density.Then,a genetic algorithm is applied to obtain a solution for the coil geometry parameters with field harmonics on the order of 10^(-4).Finally,considering the practical engineering needs of the accelerator interaction region,electromagnetic design examples of racetrack quadrupole magnets with high gradients,large apertures,and small apertures are described,and the application prospects of racetrack quadrupole coils are analyzed.
基金Project supported by the“Strategic Priority Research Program(B)”of the Chinese Academy of Sciences(Grant No.XDB04020200)the Shanghai Municipal Science and Technology Commission Project,China(Grant No.15DZ1940902)
文摘For a practical superconducting quantum interference device(SQUID) based measurement system,the Tesla/volt coefficient must be accurately calibrated.In this paper,we propose a highly efficient method of calibrating a SQUID magnetometer system using three orthogonal Helmholtz coils.The Tesla/volt coefficient is regarded as the magnitude of a vector pointing to the normal direction of the pickup coil.By applying magnetic fields through a three-dimensional Helmholtz coil,the Tesla/volt coefficient can be directly calculated from magnetometer responses to the three orthogonally applied magnetic fields.Calibration with alternating current(AC) field is normally used for better signal-to-noise ratio in noisy urban environments and the results are compared with the direct current(DC) calibration to avoid possible effects due to eddy current.In our experiment,a calibration relative error of about 6.89 × 10-4is obtained,and the error is mainly caused by the non-orthogonality of three axes of the Helmholtz coils.The method does not need precise alignment of the magnetometer inside the Helmholtz coil.It can be used for the multichannel magnetometer system calibration effectively and accurately.
基金supported by Hubei Provincial Natural Science Foundation of China(No.BZQ22006)Fundamental Research Funds for the Central Universities(No.CZY20028)+1 种基金National Magnetic Confinement Fusion Energy R&D Program of China(No.2018YFE0309102)National Natural Science Foundation of China(No.51821005)。
文摘The resonant magnetic perturbation(RMP)system is a powerful auxiliary system on tokamaks.On the J-TEXT tokamak,a set of new in-vessel coils is designed to enhance the amplitude of the RMP.The new coils are designed to be two-turn saddle coils.These two-turn saddle coils have been optimized in terms of their structure,support,and protection components to overcome the limitations of the narrow in-vessel space,resulting in a compact coil module that can be accommodated in the vessel.To verify the feasibility of this design,an electromagnetic simulation is performed to investigate the electrical parameters and the generated field of the coils.A multi-field coupled simulation is performed to investigate the capacity of heat dissipation.As a result of these efforts,the new RMP coils have been successfully installed on the J-TEXT tokamak.It has significantly enhanced the RMP amplitude and been widely applied in experiments.
基金This work is funded by the Magnetic Resonance Union of the Chinese Academy of Sciences(Grant No.2021gzl002)the International Partnership Program of Chinese Academy of Sciences(Grant No.182111KYSB20210014)+1 种基金the National Science Foundation of China(Grant No.52293423,Grant No.52277031)the Research and Development of Key Technologies and Equipment for Major Science and Technology Infrastructure of Development and Reform Commission of Shenzhen Municipality,China(Grant No.ZDKJ20190305002).
文摘The relatively fragile low-temperature stability of cryogen-free superconducting magnetic resonance imaging(MRI)magnets requires the careful management of exogenous heat sources.A strongly shielded gradient magnetic field is important for the optimal operation of cryogen-free MRI systems.In this study,we present an enhanced shielding method incorporating a regionalized stray field constraining strategy.By optimizing the constraint parameters,we could develop engineering-feasible gradient coil schemes without increasing system complexity but with the stray field intensity reduced by half.In real measurement in an integrated MRI system,the developed gradient assembly demonstrated good performance and supported to output images of excellent quality.Our findings suggested that the proposed method could potentially form a useful design paradigm for cryogen-free MRI magnets.
基金supported by the Scientific Research Foundation of Xijing University,China(No.XJ19T03)the Opening Project of Science and Technology on Reliability Physics and Application Technology of Electronic Component Laboratory(No.ZHD201701)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2024JC-YBMS-342).
文摘Enhancing plasma uniformity can be achieved by modifying coil and chamber structures in radio frequency inductively coupled plasma(ICP)to meet the demand for large-area and uniformly distributed plasma in industrial manufacturing.This study utilized a two-dimensional self-consistent fluid model to investigate how different coil configurations and chamber aspect ratios affect the radial uniformity of plasma in radio frequency ICP.The findings indicate that optimizing the radial spacing of the coil enhances plasma uniformity but with a reduction in electron density.Furthermore,optimizing the coil within the ICP reactor,using the interior point method in the Interior Point Optimizer significantly enhances plasma uniformity,elevating it from 56%to 96%within the range of the model sizes.Additionally,when the chamber aspect ratio k changes from 2.8 to 4.7,the plasma distribution changes from a center-high to a saddleshaped distribution.Moreover,the plasma uniformity becomes worse.Finally,adjusting process parameters,such as increasing source power and gas pressure,can enhance plasma uniformity.These findings contribute to optimizing the etching process by improving plasma radial uniformity.
基金supported by the National Key R&D Program of China (2022YFA1603001,2021YFC2801402)the National Nature Science Foundation of China (12073053)the Science and Technology Plan of Inner Mongolia (2021GG0245).
文摘Research on adaptive deformable mirror technology for voice coil actuators(VCAs)is an important trend in the development of large ground-based telescopes.A voice coil adaptive deformable mirror contains a large number of actuators,and there are problems with structural coupling and large temperature increases in their internal coils.Additionally,parameters of the traditional proportional integral derivative(PID)control cannot be adjusted in real-time to adapt to system changes.These problems can be addressed by introducing fuzzy control methods.A table lookup method is adopted to replace real-time calculations of the regular fuzzy controller during the control process,and a prototype platform has been established to verify the effectiveness and robustness of this process.Experimental tests compare the control performance of traditional and fuzzy proportional integral derivative(Fuzzy-PID)controllers,showing that,in system step response tests,the fuzzy control system reduces rise time by 20.25%,decreases overshoot by 78.24%,and shortens settling time by 67.59%.In disturbance rejection experiments,fuzzy control achieves a 46.09%reduction in the maximum deviation,indicating stronger robustness.The Fuzzy-PID controller,based on table lookup,outperforms the standard controller significantly,showing excellent potential for enhancing the dynamic performance and disturbance rejection capability of the voice coil motor actuator system.
文摘In global industrialization, efforts have been made to increase the rate of heat transfer in heat exchanger, minimizing the size of heat exchanger to reduce cost as well as increasing the effectiveness. Helical coil heat exchanger (HCHE) has been proven to be effective in improving heat transfer due to its large surface area. In this study, HCHE was designed to provide hot air needed for fluidized bed drying processes. The HCHE design model was fabricated and evaluated to study the efficiency of the hot air output for a laboratory fluidized bed dryer. The mathematical model for estimation of the final (output) temperature of air, Taf, passing through the HCHE was developed and validated experimentally. The drying of bitter kola particulates was carried out with a drying temperature of 50C 3C and a bed height-to-bed diameter ratio (H/D) of 1.5. The time taken to dry bitter kola particulates to 0.4% moisture content was 1 hour 45 minutes. Hence, HCHE is recommended for use in the production of hot for laboratory-scale fluidized bed dryers.
基金supported by the National Natural Science Foundation of China(52261160384)the Shenzhen Science and Technology Innovation Commission(RCYX20221008092934093)+1 种基金the Shenzhen Science and Technology Program(KJZD20230923114107014)the support from Testing Technology Center of Materials and Devices,Tsinghua Shenzhen International Graduate School。
文摘The development of aqueous Zn batteries is limited by parasitic water reactions,corrosion,and dendrite growth.To address these challenges,an inner Helmholtz plane(IHP)regulation method is proposed by employing low-cost,non-toxic maltitol as the electrolyte additive.The preferential adsorption behavior of maltitol can expel the water from the inner Helmholtz plane,and thus hinder the immediate contact between Zn metal and H_(2)O.Meanwhile,strong interaction between maltitol and H_(2)O molecules can restrain the activity of H_(2)O.Besides,the"IHP adsorption effect"along with the low LUMO energy level of maltitol-CF_(3)SO_(3)^(-)can promote the in-situ formation of an organic-inorganic complex solid electrolyte interface(SEI)layer.As a result,the hydrogen/oxygen evolution side reaction,corrosion,and dendrites issues are effectively suppressed,thereby leading to highly reversible and dendrite-free Zn plating/stripping.The Zn‖I_(2)battery with hybrid electrolytes also demonstrates high electrochemical performance and ultralong cycling stability,showing a capacity retention of 75%over 20000 charge-discharge cycles at a large current density of 5 A g^(-1).In addition,the capacity of the device has almost no obvious decay over20000 cycles even at-30℃.This work offers a successful electrolyte regulation strategy via the IHP adsorption effect to design electrolytes for high-performance rechargeable Zn-ion batteries.
基金Supported by Science Fund for Creative Research Groups of National Natural Science Foundation of China(Grant No.51221004)National Natural Science Foundation of China(Grant No.50805127)Fundamental Research Funds for the Central Universities of China(Grant No.2011QNA4002)
文摘The methods of improving the dynamic performance of high speed on/off solenoid valve include increasing the magnetic force of armature and the slew rate of coil current, decreasing the mass and stroke of moving parts. The increase of magnetic force usually leads to the decrease of current slew rate, which could increase the delay time of the dynamic response of solenoid valve. Using a high voltage to drive coil can solve this contradiction, but a high driving voltage can also lead to more cost and a decrease of safety and reliability. In this paper, a new scheme of parallel coils is investigated, in which the single coil of solenoid is replaced by parallel coils with same ampere turns. Based on the mathematic model of high speed solenoid valve, the theoretical formula for the delay time of solenoid valve is deduced. Both the theoretical analysis and the dynamic simulation show that the effect of dividing a single coil into N parallel sub-coils is close to that of driving the single coil with N times of the original driving voltage as far as the delay time of solenoid valve is concerned. A specific test bench is designed to measure the dynamic performance of high speed on/off solenoid valve. The experimental results also prove that both the delay time and switching time of the solenoid valves can be decreased greatly by adopting the parallel coil scheme. This research presents a simple and practical method to improve the dynamic performance of high speed on/off solenoid valve.
基金Project supported by the National Nature Science Foundation of China (Grant No. 30900332)Grant of General Administration of Quality Supervision Inspection and Quarantine of China (Grant No. 201210079)+1 种基金the Program for Science and Technology Department of Zhejiang Province, China (Grant Nos. 2010C14010 and 2010C33172)the Natural Science Foundation of Zhejiang Province, China (Grant No. Y2090966)
文摘In this paper, an approach to the design of shielded radio-frequency (RF) phased-array coils for magnetic resonance imaging (MRI) is proposed. The target field method is used to find current densities distributed on primary and shield coils. The stream function technique is used to discretize current densities and to obtain the winding patterns of the coils. The corresponding highly ill-conditioned integral equation is solved by the Tikhonov regularization with a penalty function related to the minimum curvature. To balance the simplicity and smoothness with the homogeneity of the magnetic field of the coll's winding pattern, the selection of a penalty factor is discussed in detail.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60871001)
文摘For a superconducting magnet of magnetic resonance imaging (MRI), the novel approach presented in this paper allows the design of cylindrical gradient and shim coils of finite length. The method is based on identification of the weighting of harmonic components in the current distribution that will generate a magnetic field whose z-component follows a chosen spherical harmonic function. Mathematical expressions which relate the harmonic terms in the cylin- drical current distribution to spherical harmonic terms in the field expansion are established. Thus a simple matrix inversion approach can be used to design a shim coil of any order pure harmonic. The expressions providing a spherical harmonic decomposition of the field components produced by a particular cylindrical current distribution are novel. A stream function was applied to obtain the discrete wire distribution on the cylindrical-surface. This method does not require the setting of the target-field points. The discussion referring to matrix equations in terms of condition numbers proves that this novel approach has no ill-conditioned problems. The results also indicate that it can be used to design cylindrical-surface shim coils of finite length that will generate a field variation which follows a particular spherical harmonic over a reasonably large-sized volume.