Lectures on the Free Electron Laser Theory and Related Topics

Dattoli, G.; Renieri, A.; Torre, A.

doi:10.1142/1334

Cited by 117 publications

(122 citation statements)

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“…A large number of functions are recognized as belonging to the BF family. Many variable BF were introduced at the beginning of the last century, see for example [1,11], forgotten for many years and reconsidered within the context of various physical applications at the end of the last century, see for example [2][3][4][5][6][7][8].…”

Section: Discussionmentioning

confidence: 99%

“…Dattoli and his co-workers introduced and discussed various generalizations of BF within purely mathematical and applicative contexts (see for example [2][3][4][5][6][7][8]). Generalized Bessel functions (GBF) have become a powerful tool to investigate the dynamical aspects of physical This is the most convenient form to study the modified forms of the first-kind cylindrical GBF.…”

Section: Introductionmentioning

confidence: 99%

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Representation of Lie algebra T3 and 2-variable 2-parameter Bessel functions

Khan¹,

Yasmin

Mittal³

2007

Journal of Mathematical Analysis and Applications

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In this paper, we deal with the problem of framing 2-variable 2-parameter Bessel functions (2V2PBF) into the context of the representation Q(w, m 0 ) of the 3-dimensional Lie algebra T 3 . Further, we derive generating relations and identities involving 2V2PBF. Furthermore, we deduce some new and known relations involving various other forms of generalized Bessel functions (GBF) and Bessel functions (BF) as applications of these results.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Representation of Lie algebra T3 and 2-variable 2-parameter Bessel functions

Khan¹,

Yasmin

Mittal³

2007

Journal of Mathematical Analysis and Applications

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“…The magneto-static wiggler field in a free-electron laser is generally expressed by [1][2][3][4][5][6][7][8][9][10] B w ðzÞ ¼ẽ x B w cos k w z ð ÞÀẽ y B w sin k w z ð Þ;…”

Section: Modulation On Motion Of Relativistic Electronsmentioning

confidence: 99%

Field Distribution of a Planar Electrostatic Wiggler and Modulation Effect on the Motion of Relativistic Electrons

Zhang

2009

J Infrared Milli Terahz Waves

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A planar electrostatic wiggler is formed by two parallel metallic plates, where the upper-plate is corrugated with sinusoidal ripples and connected to a negative voltage and the lower-plate is smooth and grounded. The field distribution is mathematically derived in detail. It is demonstrated that this planar electrostatic wiggler can efficiently modulate the motion of relativistic electrons just as a magneto-static wiggler does in a free-electron laser. Results obtained here will provide basis to analyze the amplification mechanism of a fast wave by a relativistic electron beam in a planar electrostatic wiggler.

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“…(1) is accurate only near to the axis otherwise they do not satisfy MaxwellÕs equation. At the lowest order in the transverse co-ordinates, the field components read [12]:…”

Section: Undulator Radiation and Off-axis Motionmentioning

confidence: 99%