title: Magnetostatic focal spot correction for x-ray tubes operating in strong magnetic fields using iterative optimization.
abstract: OBJECTIVE
  Combining x-ray fluoroscopy and MR imaging systems for guidance of interventional procedures has become more commonplace. By designing an x-ray tube that is immune to the magnetic fields outside of the MR bore, the two systems can be placed in close proximity to each other. A major obstacle to robust x-ray tube design is correcting for the effects of the magnetic fields on the x-ray tube focal spot. A potential solution is to design active shielding that locally cancels the magnetic fields near the focal spot.
  
  
  METHODS
  An iterative optimization algorithm is implemented to design resistive active shielding coils that will be placed outside the x-ray tube insert. The optimization procedure attempts to minimize the power consumption of the shielding coils while satisfying magnetic field homogeneity constraints. The algorithm is composed of a linear programming step and a nonlinear programming step that are interleaved with each other. The coil results are verified using a finite element space charge simulation of the electron beam inside the x-ray tube. To alleviate heating concerns an optimized coil solution is derived that includes a neodymium permanent magnet. Any demagnetization of the permanent magnet is calculated prior to solving for the optimized coils. The temperature dynamics of the coil solutions are calculated using a lumped parameter model, which is used to estimate operation times of the coils before temperature failure.
  
  
  RESULTS
  For a magnetic field strength of 88 mT, the algorithm solves for coils that consume 588 A∕cm(2). This specific coil geometry can operate for 15 min continuously before reaching temperature failure. By including a neodymium magnet in the design the current density drops to 337 A∕cm(2), which increases the operation time to 59 min. Space charge simulations verify that the coil designs are effective, but for oblique x-ray tube geometries there is still distortion of the focal spot shape along with deflections of approximately 3 mm in the radial and circumferential directions on the anode.
  
  
  CONCLUSIONS
  Active shielding is an attractive solution for correcting the effects of magnetic fields on the x-ray focal spot. If extremely long fluoroscopic exposure times are required, longer operation times can be achieved by including a permanent magnet with the active shielding design.
authors.affiliation: Department of Radiology, Stanford University, Stanford, CA, USA. plillane@gmail.com
authors.forename: Prasheel
authors.initials: P
authors.lastname: Lillaney
authors.forename: Mihye
authors.initials: M
authors.lastname: Shin
authors.forename: Steven M
authors.initials: SM
authors.lastname: Conolly
authors.forename: Rebecca
authors.initials: R
authors.lastname: Fahrig
mesh_terms: D005240:Feasibility Studies; D060526:Magnetic Fields; D008279:Magnetic Resonance Imaging / Q000295:instrumentation*; D059346:Magnets; D013696:Temperature; D014965:X-Rays