title: Electrostatic focal spot correction for x-ray tubes operating in strong magnetic fields.
abstract: OBJECTIVE
  A close proximity hybrid x-ray/magnetic resonance (XMR) imaging system offers several critical advantages over current XMR system installations that have large separation distances (∼5 m) between the imaging fields of view. The two imaging systems can be placed in close proximity to each other if an x-ray tube can be designed to be immune to the magnetic fringe fields outside of the MR bore. One of the major obstacles to robust x-ray tube design is correcting for the effects of the MR fringe field on the x-ray tube focal spot. Any fringe field component orthogonal to the x-ray tube electric field leads to electron drift altering the path of the electron trajectories.
  
  
  METHODS
  The method proposed in this study to correct for the electron drift utilizes an external electric field in the direction of the drift. The electric field is created using two electrodes that are positioned adjacent to the cathode. These electrodes are biased with positive and negative potential differences relative to the cathode. The design of the focusing cup assembly is constrained primarily by the strength of the MR fringe field and high voltage standoff distances between the anode, cathode, and the bias electrodes. From these constraints, a focusing cup design suitable for the close proximity XMR system geometry is derived, and a finite element model of this focusing cup geometry is simulated to demonstrate efficacy. A Monte Carlo simulation is performed to determine any effects of the modified focusing cup design on the output x-ray energy spectrum.
  
  
  RESULTS
  An orthogonal fringe field magnitude of 65 mT can be compensated for using bias voltages of +15 and -20 kV. These bias voltages are not sufficient to completely correct for larger orthogonal field magnitudes. Using active shielding coils in combination with the bias electrodes provides complete correction at an orthogonal field magnitude of 88.1 mT. Introducing small fields (<10 mT) parallel to the x-ray tube electric field in addition to the orthogonal field does not affect the electrostatic correction technique. However, rotation of the x-ray tube by 30° toward the MR bore increases the parallel magnetic field magnitude (∼72 mT). The presence of this larger parallel field along with the orthogonal field leads to incomplete correction. Monte Carlo simulations demonstrate that the mean energy of the x-ray spectrum is not noticeably affected by the electrostatic correction, but the output flux is reduced by 7.5%.
  
  
  CONCLUSIONS
  The maximum orthogonal magnetic field magnitude that can be compensated for using the proposed design is 65 mT. Larger orthogonal field magnitudes cannot be completely compensated for because a pure electrostatic approach is limited by the dielectric strength of the vacuum inside the x-ray tube insert. The electrostatic approach also suffers from limitations when there are strong magnetic fields in both the orthogonal and parallel directions because the electrons prefer to stay aligned with the parallel magnetic field. These challenging field conditions can be addressed by using a hybrid correction approach that utilizes both active shielding coils and biasing electrodes.
authors.affiliation: Department of Radiology and Biomedical Imaging, University of California San Francisco, San Francisco, California 94107.
authors.forename: Prasheel
authors.initials: P
authors.lastname: Lillaney
authors.affiliation: Department of Radiology, Stanford University, Stanford, California 94305 and Department of Mechanical Engineering, Stanford University, Stanford, California 94305.
authors.forename: Mihye
authors.initials: M
authors.lastname: Shin
authors.affiliation: Department of Radiology, Stanford University, Stanford, California 94305.
authors.forename: Waldo
authors.initials: W
authors.lastname: Hinshaw
authors.affiliation: Department of Radiology, Stanford University, Stanford, California 94305.
authors.forename: Rebecca
authors.initials: R
authors.lastname: Fahrig
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004566:Electrodes; D004583:Electrons; D004867:Equipment Design; D005471:Fluoroscopy / Q000295:instrumentation / Q000379:methods; D060526:Magnetic Fields; D008279:Magnetic Resonance Imaging / Q000379:methods; D008280:Magnetics; D009010:Monte Carlo Method; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D055672:Static Electricity; D014965:X-Rays