Abstract

Undulators are the most advanced sources for the generation of synchrotron radiation. The photons generated by a single electron add up coherently along the electron trajectory. In order to do so, the oscillatory motion of the electron has to be in phase with the emitted photons along the whole undulator. Small magnetic errors can cause unwanted destructive interferences. In standard permanent magnet undulators, the magnetic errors are reduced by applying shimming techniques. Superconductive undulators have higher magnetic fields than permanent magnet undulators but shimming is more complex. In this paper it is shown that coupled superconductive loops installed along the surface of the superconductive undulator coil can significantly reduce the destructive effect of the field errors. This new idea might allow the building of undulators with a superior field quality.

Highlights

  • Undulators are the most effective sources for brilliant x rays in storage rings

  • The maximum magnetic field strength of permanent magnet undulators is limited by the material properties of the permanent magnets [1,2]

  • After first experiments in the 1970’s [6,7], the development was resumed in the early 1990’s [8,9] and several intermediate steps were followed by the installation of a 100 period superconductive undulator with a period length of 14 mm in the storage ring ANKA in April 2005 [10,11]

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Summary

INTRODUCTION

Undulators are the most effective sources for brilliant x rays in storage rings. Up to now undulators were mainly made from permanent magnets. After first experiments in the 1970’s [6,7], the development was resumed in the early 1990’s [8,9] and several intermediate steps were followed by the installation of a 100 period superconductive undulator with a period length of 14 mm in the storage ring ANKA in April 2005 [10,11] This device made it possible to study the properties of the emitted radiation [12], the beam heat load [13], the effect of the undulator on the orbit [14], the field errors, and the development of correction schemes for field errors [15,16]. This provided the stimulation to think about concepts for superconductive undulators where field errors are compensated automatically without additional steps of shimming [23]

INDUCTION SHIMMING
One period with closed loop
Generalization for n overlapping closed loops
GENERALIZATION FOR BIOT-SAVART CLOSED LOOPS
Faraday’s law for overlapping closed loops in a long undulator
Biot-Savart’s law for overlapping closed loops in a long undulator
SIMULATIONS
Correction of a single field error
Monte Carlo simulations
Findings
CONCLUSION
Full Text
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