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Outline

Simultaneous Two-Ion Mass Spectroscopy

1995

Abstract

Abstract It is possible to compare the masses of single ions with an accuracy of one part in 1011 (an order of magnitude better than the current state of the art) by comparing the cyclotron frequencies of two ions of different species confined simultaneously in a Penning trap. Computer simulations were used to study the motion of two simultaneously trapped ions in a trap with predicted, partially controllable, imperfections; the results were checked against theoretical predictions for ideal Penning traps.

References (36)

  1. *az1r,z1i+hdt*az1i, z2r+hdt*az2r,z2i+hdt*az2i, er+hdt*aer,ei+hdt*aei);
  2. *dy2)(x1+hdt*ax1,y1+hdt*ay1,x2+hdt*ax2,y2+hdt*ay2, z1r+hdt*az1r,z1i+hdt*az1i, z2r+hdt*az2r,z2i+hdt*az2i, er+hdt*aer,ei+hdt*aei);
  3. ¡ ¥ bz1r=(*dz1r)(x1+hdt*ax1,y1+hdt*ay1,x2+hdt*ax2,y2+hdt*ay2, z1r+hdt*az1r,z1i+hdt*az1i, z2r+hdt*az2r,z2i+hdt*az2i, er+hdt*aer,ei+hdt*aei);
  4. *dz1i)(x1+hdt*ax1,y1+hdt*ay1,x2+hdt*ax2,y2+hdt*ay2, z1r+hdt*az1r,z1i+hdt*az1i, z2r+hdt*az2r,z2i+hdt*az2i, er+hdt*aer,ei+hdt*aei);
  5. *dz2r)(x1+hdt*ax1,y1+hdt*ay1,x2+hdt*ax2,y2+hdt*ay2, z1r+hdt*az1r,z1i+hdt*az1i, z2r+hdt*az2r,z2i+hdt*az2i, er+hdt*aer,ei+hdt*aei);
  6. *dz2i)(x1+hdt*ax1,y1+hdt*ay1,x2+hdt*ax2,y2+hdt*ay2, ¢ ¥ z1r+hdt*az1r,z1i+hdt*az1i, z2r+hdt*az2r,z2i+hdt*az2i, er+hdt*aer,ei+hdt*aei);
  7. ber=(*der)(x1+hdt*ax1,y1+hdt*ay1,x2+hdt*ax2,y2+hdt*ay2, z1r+hdt*az1r,z1i+hdt*az1i, z2r+hdt*az2r,z2i+hdt*az2i, er+hdt*aer,ei+hdt*aei);
  8. bei=(*dei)(x1+hdt*ax1,y1+hdt*ay1,x2+hdt*ax2,y2+hdt*ay2, z1r+hdt*az1r,z1i+hdt*az1i, z2r+hdt*az2r,z2i+hdt*az2i, er+hdt*aer,ei+hdt*aei);
  9. *dx1)(x1+hdt*bx1,y1+hdt*by1,x2+hdt*bx2,y2+hdt*by2, £ ¥ z1r+hdt*bz1r,z1i+hdt*bz1i, z2r+hdt*bz2r,z2i+hdt*bz2i, er+hdt*ber,ei+hdt*bei);
  10. *dy1)(x1+hdt*bx1,y1+hdt*by1,x2+hdt*bx2,y2+hdt*by2, z1r+hdt*bz1r,z1i+hdt*bz1i, z2r+hdt*bz2r,z2i+hdt*bz2i, er+hdt*ber,ei+hdt*bei);
  11. *dx2)(x1+hdt*bx1,y1+hdt*by1,x2+hdt*bx2,y2+hdt*by2, z1r+hdt*bz1r,z1i+hdt*bz1i, z2r+hdt*bz2r,z2i+hdt*bz2i, er+hdt*ber,ei+hdt*bei);
  12. *dy2)(x1+hdt*bx1,y1+hdt*by1,x2+hdt*bx2,y2+hdt*by2, z1r+hdt*bz1r,z1i+hdt*bz1i, z2r+hdt*bz2r,z2i+hdt*bz2i, ¤ ¥ er+hdt*ber,ei+hdt*bei);
  13. *dz1r)(x1+hdt*bx1,y1+hdt*by1,x2+hdt*bx2,y2+hdt*by2, z1r+hdt*bz1r,z1i+hdt*bz1i, z2r+hdt*bz2r,z2i+hdt*bz2i, er+hdt*ber,ei+hdt*bei);
  14. *dz1i)(x1+hdt*bx1,y1+hdt*by1,x2+hdt*bx2,y2+hdt*by2, z1r+hdt*bz1r,z1i+hdt*bz1i, z2r+hdt*bz2r,z2i+hdt*bz2i, er+hdt*ber,ei+hdt*bei);
  15. *dz2r)(x1+hdt*bx1,y1+hdt*by1,x2+hdt*bx2,y2+hdt*by2, z1r+hdt*bz1r,z1i+hdt*bz1i, z2r+hdt*bz2r,z2i+hdt*bz2i, er+hdt*ber,ei+hdt*bei);
  16. ¥ cz2i=(*dz2i)(x1+hdt*bx1,y1+hdt*by1,x2+hdt*bx2,y2+hdt*by2, z1r+hdt*bz1r,z1i+hdt*bz1i, z2r+hdt*bz2r,z2i+hdt*bz2i, er+hdt*ber,ei+hdt*bei);
  17. cer=(*der)(x1+hdt*bx1,y1+hdt*by1,x2+hdt*bx2,y2+hdt*by2, z1r+hdt*bz1r,z1i+hdt*bz1i, z2r+hdt*bz2r,z2i+hdt*bz2i, er+hdt*ber,ei+hdt*bei);
  18. cei=(*dei)(x1+hdt*bx1,y1+hdt*by1,x2+hdt*bx2,y2+hdt*by2, z1r+hdt*bz1r,z1i+hdt*bz1i, z2r+hdt*bz2r,z2i+hdt*bz2i, er+hdt*ber,ei+hdt*bei);
  19. ¤ ¦¥ ¥ ex1=(*dx1)(x1+dt*cx1,y1+dt*cy1,x2+dt*cx2,y2+dt*cy2, z1r+dt*cz1r,z1i+dt*cz1i, z2r+dt*cz2r,z2i+dt*cz2i, er+dt*cer,ei+dt*cei);
  20. *dy1)(x1+dt*cx1,y1+dt*cy1,x2+dt*cx2,y2+dt*cy2, z1r+dt*cz1r,z1i+dt*cz1i, z2r+dt*cz2r,z2i+dt*cz2i, er+dt*cer,ei+dt*cei);
  21. *dx2)(x1+dt*cx1,y1+dt*cy1,x2+dt*cx2,y2+dt*cy2, z1r+dt*cz1r,z1i+dt*cz1i, z2r+dt*cz2r,z2i+dt*cz2i, er+dt*cer,ei+dt*cei);
  22. *dy2)(x1+dt*cx1,y1+dt*cy1,x2+dt*cx2,y2+dt*cy2, ¤ ¤ ¦¥ z1r+dt*cz1r,z1i+dt*cz1i, z2r+dt*cz2r,z2i+dt*cz2i, er+dt*cer,ei+dt*cei);
  23. *dz1r)(x1+dt*cx1,y1+dt*cy1,x2+dt*cx2,y2+dt*cy2, z1r+dt*cz1r,z1i+dt*cz1i, z2r+dt*cz2r,z2i+dt*cz2i, er+dt*cer,ei+dt*cei);
  24. *dz1i)(x1+dt*cx1,y1+dt*cy1,x2+dt*cx2,y2+dt*cy2, z1r+dt*cz1r,z1i+dt*cz1i, z2r+dt*cz2r,z2i+dt*cz2i, er+dt*cer,ei+dt*cei);
  25. *dz2r)(x1+dt*cx1,y1+dt*cy1,x2+dt*cx2,y2+dt*cy2, z1r+dt*cz1r,z1i+dt*cz1i, z2r+dt*cz2r,z2i+dt*cz2i, ¤ § ¥ er+dt*cer,ei+dt*cei);
  26. *dz2i)(x1+dt*cx1,y1+dt*cy1,x2+dt*cx2,y2+dt*cy2, z1r+dt*cz1r,z1i+dt*cz1i, z2r+dt*cz2r,z2i+dt*cz2i, er+dt*cer,ei+dt*cei);
  27. eer=(*der)(x1+dt*cx1,y1+dt*cy1,x2+dt*cx2,y2+dt*cy2, z1r+dt*cz1r,z1i+dt*cz1i, z2r+dt*cz2r,z2i+dt*cz2i, er+dt*cer,ei+dt*cei);
  28. eei=(*dei)(x1+dt*cx1,y1+dt*cy1,x2+dt*cx2,y2+dt*cy2, z1r+dt*cz1r,z1i+dt*cz1i, z2r+dt*cz2r,z2i+dt*cz2i, er+dt*cer,ei+dt*cei);
  29. ¤ ¨¥ fx1=(ax1+bx1+bx1+cx1+cx1+ex1) 6.0; fy1=(ay1+by1+by1+cy1+cy1+ey1) 6.0; fx2=(ax2+bx2+bx2+cx2+cx2+ex2) 6.0; fy2=(ay2+by2+by2+cy2+cy2+ey2) 6.0; fz1r=(az1r+bz1r+bz1r+cz1r+cz1r+ez1r) 6.0; fz1i=(az1i+bz1i+bz1i+cz1i+cz1i+ez1i) 6.0; fz2r=(az2r+bz2r+bz2r+cz2r+cz2r+ez2r) 6.0;
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