Radiation attenuation

Radiation attenuation is a reduction in the amplitude of transverse betatron vibrations of a charged particle in a cyclic accelerator , as well as in the emittance of a particle beam associated with synchrotron radiation . Since the intensity of synchrotron radiation is very dependent on the particle energy (~ γ ⁴ ), radiation attenuation is important for accelerators of light ultrarelativistic particles (electron synchrotrons ), and is not significant for hadron machines.

Content

1 attenuation mechanism
2 Attenuation limit
3 damping rings
4 See also
5 notes
6 References

Attenuation Mechanism

Radiation of an ultrarelativistic particle in a transverse magnetic field occurs in the direction of particle motion, in a narrow cone with a solution of ~ 1 / γ. Accordingly, during emission, all components of the particle momentum, both longitudinal and transverse, are reduced. As the accelerating cavity passes, the particle makes up for the energy lost by the radiation, however, since the electric field is directed along the beam axis, only the longitudinal component of the pulse is restored. Thus, the transverse momentum of the particle decreases with each revolution, the transverse angle y '= p _y / p ₀ (y = x, z) is reduced, and the Courant-Snyder invariant , that is, the amplitude of betatron vibrations.

Since the energy U ₀ radiated per revolution is always much less than the particle energy E ₀ , the radiation attenuation is relatively slow. The damping decrement ζ depends on the energy and on the fields of magnetic elements located in the orbit of the beam. The decay times τ = 1 / ζ can be calculated as follows ^[1] :

$\tau _{x}=2{\frac {E_{0}}{J_{x}U_{0}}}T_{0}$ ${\ displaystyle \ tau _ {x} = 2 {\ frac {E_ {0}} {J_ {x} U_ {0}}} T_ {0}}$ ,
$\tau _{z}=2{\frac {E_{0}}{U_{0}}}T_{0}$ ${\ displaystyle \ tau _ {z} = 2 {\ frac {E_ {0}} {U_ {0}}} T_ {0}}$ ,
$\tau _{s}=2{\frac {E_{0}}{J_{E}U_{0}}}T_{0}$ ${\ displaystyle \ tau _ {s} = 2 {\ frac {E_ {0}} {J_ {E} U_ {0}}} T_ {0}}$ ,

where E ₀ is the electron energy, U ₀ is the energy loss per revolution, T ₀ is the beam revolution period, J _{x, z, E} are the dimensionless attenuation decrements of three degrees of freedom:

$J_{E}=2+I_{4}/I_{2}$ ${\ displaystyle J_ {E} = 2 + I_ {4} / I_ {2}}$ ,
$J_{x}=1-I_{4}/I_{2}$ ${\ displaystyle J_ {x} = 1-I_ {4} / I_ {2}}$ ,
$J_{x}+J_{z}+J_{E}=4$ ${\ displaystyle J_ {x} + J_ {z} + J_ {E} = 4}$ .

(The last equality is called the Decrement Sum Theorem .) The radiation integrals I _{2,4 are} determined by the focusing structure of the ring.

$I_{2}=\oint {{\frac {1}{\rho (s)}}ds}$ ${\ displaystyle I_ {2} = \ oint {{\ frac {1} {\ rho (s)}} ds}}$ ,
$I_{4}=\oint {{\frac {D(s)}{\rho (s)}}\left({\frac {1}{\rho (s)^{2}}}+2k_{1}(s)\right)}$ ${\ displaystyle I_ {4} = \ oint {{\ frac {D (s)} {\ rho (s)}} left ({\ frac {1} {\ rho (s) ^ {2}}} + 2k_ {1} (s) \ right)}}$ .

Here ρ is the local curvature of the orbit, D is the dispersion function, k ₁ = G / Bρ is the quadrupole component of the magnetic field in the rotary magnet , G is the field gradient, Bρ is the magnetic rigidity .

Attenuation Limit

An important role in the attenuation is played by the quantum nature of synchrotron radiation. Fluctuations in the radiation of individual quanta lead to a buildup of betatron oscillations. The final oscillation amplitude of the circulating particle is determined by the balance between the mechanisms of attenuation and recoil. It should be noted that quantum fluctuations excite only longitudinal ( synchrotron ) and transverse horizontal oscillations, but not vertical, if the ring is flat. The equilibrium vertical emittance of the beam is determined by the coupling of two transverse vibrational modes. As a rule, the coupling is small, and in electron synchrotrons the beam is flat and elongated - the radial size is much larger than the vertical, and the longitudinal one is larger than the transverse ones.

Damping Rings

To obtain intense electron and positron beams with low emittance, storage rings are used . A portion of particles is injected into the storage ring, attenuation occurs, during which the emittance decreases, and part of the ring acceptance is freed for a new portion. Without dissipative forces that provide attenuation, the injection of a new portion without losing the previous is impossible, due to Liouville's theorem on the conservation of phase volume .

To reduce the decay time, and sometimes to redistribute the decay decrements between the longitudinal and radial degrees of freedom, emitting wigglers — strong-field magnetic elements that multiply the particle’s energy loss by radiation — are often installed in damping rings.

The damping rings are widely used both in accelerator complexes for experiments in high-energy physics , for the preparation of intense beams for cyclic and linear colliders , and for experiments with an extracted beam, and as sources of synchrotron radiation . Since it is important for a SR source to obtain a high radiation brightness, it is necessary to minimize the emittance of the electron beam — the radiation source. For this, special schemes for arranging focusing elements (Double Bend Achromat, etc.) are used. However, the lower emittance limit associated with quantum fluctuations of radiation has become a fundamental obstacle to obtaining ultra-small emittances, and the most advanced projects of 4th generation SR sources are already based not on synchrotrons, but on recuperator accelerators , where the beam emittance is formed not by synchrotron radiation.

Notes

↑ The Accelerator Physics of Linear Collider Damping Rings , Andy Wolski, 2003.

Links

The Physics of Damping Rings , Kai Hock, 2008.
The Accelerator Physics of Linear Collider Damping Rings , Andy Wolski, 2003.
Introduction to the ILC Damping Rings , Andy Wolski, 2009.

[1] The Accelerator Physics of Linear Collider Damping Rings , Andy Wolski, 2003.