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Imperfections

Imperfections. Eric Prebys, FNAL. Dipole Error (or Correction). Remember this one forever. Recall our generic transfer matrix If we use a dipole to introduce a small bend Θ at one point, it will in general propagate as. Example: Local Correction (“Three Bump”).

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Imperfections

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  1. Imperfections Eric Prebys, FNAL

  2. Dipole Error (or Correction) Remember this one forever Lecture 4 - Imperfections Recall our generic transfer matrix If we use a dipole to introduce a small bend Θ at one point, it will in general propagate as

  3. Example: Local Correction (“Three Bump”) Local Bumps are an extremely powerful tool in beam tuning!! Lecture 4 - Imperfections Consider a particle going down a beam line. By using a combination of three magnets, we can localize the beam motion to one area of the line We require

  4. Controls Example Lecture 4 - Imperfections • From Fermilab “Acnet” control system • The B:xxxx labels indicateindividual trim magnet powersupplies in the FermilabBooster • Defining a “MULT: N” willgroup the N following magnet power supplies • Placing the mouse over them and turning a knobon the control panelwill increment theindividual currents accordingto the ratios shown in green

  5. Closed Orbit Distortion (“cusp”) Lecture 4 - Imperfections We place a dipole at one point in a ring which bends the beam by an amount Θ. The new equilibrium orbit will be defined by a trajectory which goes once around the ring, through the dipole, and then returns to its exact initial conditions. That is Recall that we can express the transfer matrix for a complete revolution as

  6. Lecture 4 - Imperfections Plug this back in We now propagate this around the ring

  7. Quadrupole Errors Lecture 4 - Imperfections We can express the matrix for a complete revolution at a point as If we add focusing quad at this point, we have We calculate the trace to find the new tune For small errors

  8. Total Tune Shift Lecture 4 - Imperfections The focal length associated with a local anomalous gradient is So the total tune shift is

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