1 / 17

Calculations of Liquid Hg Jet Evaluated for Realistic Magnet System

Calculations of Liquid Hg Jet Evaluated for Realistic Magnet System. This summarizes work done by various people: J. Gallardo S. Kahn R. B. Palmer P. Thieberger R. Weggel K. McDonald. Steve Kahn 31 January 2001. List of Forces, Pressures, Distortions, Deflections.

forrest-conner
Download Presentation

Calculations of Liquid Hg Jet Evaluated for Realistic Magnet System

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Calculations of Liquid HgJet Evaluated for Realistic Magnet System This summarizes work done by various people: J. Gallardo S. Kahn R. B. Palmer P. Thieberger R. Weggel K. McDonald Steve Kahn 31 January 2001 Magnetic Field Effects Simulations

  2. List of Forces, Pressures, Distortions, Deflections • Induced azimuthal Eddy current. • Radial forces: JEddyBz • Hydrostatic Pressure • Axial force • Contribution from Hydrostatic Pressure • Contribution from dBz/dz • Transverse forces and deflections • Shear forces • Transverse elliptical distortion Magnetic Field Effects Simulations

  3. Magnet System Configuration • Below is the coil configuration from Bob Weggel (21-Dec-00) • Only coils in yellow region are used in analysis, others are far enough from target that they can be ignored. Magnetic Field Effects Simulations

  4. 67 mr Obviously Not to Scale Proton beam Hg Jet 0 -45 -30 +15 -60 Begin full overlap Nozzle Targeting Schematic beam Hg Jet 100 mr Begin overlap End overlap End full overlap Magnetic Field Effects Simulations

  5. Field Calculations • In this model a pole made of Vanadium Permador steel is placed in the 20 T field to act as a nozzle. • This steel has Ms=2.4 T. (Figure shown on next transparency). • The nozzle is present to insure that the Hg jet enters the field intact. • Opera-2D is used for field calculations. • This is a 2D finite element field solver that solves the cylindrical symmetric problem. • Only the hole in the nozzle breaks cylindrical symmetry. This only has effects in the vicinity of its aperture. • The beam path is inclined with respect to the magnet axis at 67 mrad. • Justification for minimum perturbation of the beam path will be mentioned later. Magnetic Field Effects Simulations

  6. 2D Axial Symmetric Model 1006 Steel Vanadium Permador Steel Ms=2.4 T Magnetic Field Effects Simulations

  7. Saturated Pole Iron is highly saturated.  < 1.36 everywhere Magnetic Field Effects Simulations

  8. Effect of Iron Pole on Field • Graphs show a comparison of local Bz and By along Hg trajectory. • Pole is made of Vanadium Permador steel which has Ms=2.4 T. Pole Surface Magnetic Field Effects Simulations

  9. Magnetic Field in Local Coordinates • Figures show Bz and By in the local coordinate system of the Hg jet. • Local system is inclined 67 mrad to solenoid axis. • Each figure shows 5 places where the the trajectory intersects axis: • At 0 cm, 10 cm, 20 cm • Z=0 cm is 120 cm from pole face. • Z=0 cm is the far end of the target. Pole face Magnetic Field Effects Simulations

  10. Field Derivatives • Forces are proportional to field derivatives. • Figure shows dBy/dz and dBz/dz along path. • Spike indicates edge of pole • Jaggedness of curves due to finite element nature. • dB/dz is 2nd derivative of potential. Each element has quadratic variation of potential. dB/dz is constant in each element. Pole face Magnetic Field Effects Simulations

  11. Force Densities • Axial force density • averaged over radius • Axial hydrostatic pressure from radial force • averaged over radius • Numerical evaluation uses • r0 = 0.5 cm • vz= 20 m/sec • = 1106 ohm-1 m-1 (Hg) Formulae from R. Palmer’s note Magnetic Field Effects Simulations

  12. Additional Shear (or is it Torque) By F F Magnetic Field Effects Simulations

  13. Force on Coil Half Magnetic Field Effects Simulations

  14. Angular Deflection from Transverse Force • The vertical force density is • This gives • The resultant deflection per unit length is • This is plotted in figure Formulae from R. Palmer’s Note Magnetic Field Effects Simulations

  15. Integrated Angular Deflection • The figure shows d/ds and x integrated over the path length. • The Hg jet will be deflected ~0.1 mrad over the trajectory. • The spacial deflection is less than 0.15 mm over the 1.5 meter path. • Adjusting the field for the changing path has not been done. This probably is not important. Magnetic Field Effects Simulations

  16. Deceleration of Hg Jet • Green curve in figure is the total axial deceleration of the Hg jet entering the magnets: V • V(z) = V0–V • Blue curve shows the contribution from axial force, <fz >. • Red curve shows the contribution from the hydrostatic pressure resulting from the radial force, <fp>. Magnetic Field Effects Simulations

  17. Elliptic Distortions By Fx • Horizontal Force: • If there is an incline angle, By0. There can be an axial eddy current: • fx=jzBy • jz~cos • Radial Inward Force • Azimuthal eddy current gives radially inward force: • fr=jBz • Eccentricity: • = y/x  Fx/Fy Fr ~0.98 at target Magnetic Field Effects Simulations

More Related