Table Of ContentHigh Frequency Sources of
Coherent Radiation for Fusion
Plasmas
IOP Series in Plasma Physics
Series Editors
Richard Dendy
Culham Centre for Fusion Energy and the University of Warwick, UK
Uwe Czarnetzki
Ruhr-University Bochum, Germany
About the series
TheIOPPlasmaPhysicsebookseriesaimsatcomprehensivecoverageofthephysics
andapplicationsofnaturalandlaboratoryplasmas,acrossalltemperatureregimes.
Books in the series range from graduate and upper-level undergraduate textbooks,
research monographs and reviews.
The conceptual areas of plasma physics addressed in the series include:
(cid:129) Equilibrium, stability and control
(cid:129) Waves: fundamental properties, emission, and absorption
(cid:129) Nonlinear phenomena and turbulence
(cid:129) Transport theory and phenomenology
(cid:129) Laser-plasma interactions
(cid:129) Non-thermal and suprathermal particle populations
(cid:129) Beams and non-neutral plasmas
(cid:129) High energy density physics
(cid:129) Plasma-solid interactions, dusty, complex and non-ideal plasmas
(cid:129) Diagnostic measurements and techniques for data analysis
The fields of application include:
(cid:129) Nuclear fusion through magnetic and inertial confinement
(cid:129) Solar-terrestrial and astrophysical plasma environments and phenomena
(cid:129) Advanced radiation sources
(cid:129) Materials processing and functionalisation
(cid:129) Propulsion, combustion and bulk materials management
(cid:129) Interaction of plasma with living matter and liquids
(cid:129) Biological, medical and environmental systems
(cid:129) Low temperature plasmas, glow discharges and vacuum arcs
(cid:129) Plasma chemistry and reaction mechanisms
(cid:129) Plasma production by novel means
High Frequency Sources of
Coherent Radiation for Fusion
Plasmas
G Dattoli
ENEA Frascati Research Center, Frascati, Rome, Italy
E Di Palma
ENEA Frascati Research Center, Frascati, Rome, Italy
S P Sabchevski
Institute of Electronics of the Bulgarian Academy of Sciences, Sofia, Bulgaria
I P Spassovsky
ENEA Frascati Research Center, Frascati, Rome, Italy
IOP Publishing, Bristol, UK
ªIOPPublishingLtd2021
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PatentsAct1988.
ISBN 978-0-7503-2464-9(ebook)
ISBN 978-0-7503-2462-5(print)
ISBN 978-0-7503-2465-6(myPrint)
ISBN 978-0-7503-2463-2(mobi)
DOI 10.1088/978-0-7503-2464-9
Version:20210801
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Contents
Preface viii
Author biographies x
Operators properties xii
Part I Fusion plasma generalities
1 Magnetically confined plasma for fusion energy 1-1
1.1 Worldwide energy needs and fusion plants 1-1
1.2 Fusion products and energy balance 1-6
1.3 Magnetic field and confinement 1-9
1.4 Magnetic mirror and confinement 1-17
1.5 Plasma as a state of matter 1-21
1.6 Plasma kinetic theory 1-27
1.7 Ohmic heating 1-29
References 1-35
2 MHD models, plasma equilibrium and instabilities 2-1
2.1 Introduction 2-1
2.2 Fusion reaction in the Sun and associated energy production 2-6
2.3 Elements of magnetohydrodynamics and plasma physics 2-10
2.4 Liouville, Vlasov and Boltzmann equations and ideal MHD 2-15
2.5 Plasma MHD phenomenology: a qualitative picture 2-19
2.6 Magnetic field Hamiltonian and rotational transform 2-30
2.7 Toroidal MHD equilibrium 2-35
2.8 The Stellarator 2-36
2.9 MHD plasma instabilities 2-41
References 2-47
3 Plasma additional heating and Tokamak engineering issues 3-1
3.1 Introduction 3-1
3.2 Plasma scaling formulae and ohmic heating 3-7
3.3 Magnetic fusion heating devices: the neutral beam injection 3-9
3.4 Radio frequency plasma heating: a few preliminaries 3-18
3.4.1 Cold magnetized plasma 3-19
3.4.2 Hot magnetized plasma 3-25
v
HighFrequencySourcesofCoherentRadiationforFusionPlasmas
3.5 The physics of radio frequency plasma heating 3-29
3.6 Generalities on beam plasma energy transfer 3-34
3.7 The mechanism of radio frequency–plasma interaction 3-39
3.8 X-mode and O-mode transfer power 3-51
3.9 Practical formulae for plasma physics and fusion devices 3-55
3.9.1 Scaling 3-61
References 3-64
Part II External additional heating sources
4 Undulator based free electron laser 4-1
4.1 Introduction 4-1
4.2 Undulator based FEL, generalities 4-2
4.3 U-FEL and other free electron sources of coherent electromagnetic 4-6
radiation
4.4 Free electron laser phenomenology and gain 4-9
4.5 FEL low and high gain regimes 4-11
4.6 Non-linear regime and saturation 4-19
4.7 Free electron laser oscillators 4-25
4.8 High gain FELs and self-amplified-spontaneous emission devices: 4-29
generalities
References 4-32
5 An overview of the gyrotron theory 5-1
5.1 Introduction 5-1
5.2 Basic physical principles of gyrotron operation 5-3
5.2.1 Cyclotron resonance 5-3
5.2.2 Azimuthal bunching of the electrons 5-6
5.2.3 Beam-wave synchronism and Brillouin diagram 5-7
5.2.4 Types of gyro-devices 5-9
5.2.5 The efficiency of the interaction and output power 5-10
5.2.6 Mode selection and coupling factor 5-13
5.2.7 Different approaches and physical models describing the 5-15
operation of the gyrotron
5.2.8 Physical models in the framework of the relativistic 5-16
electrodynamics
5.3 Electron-optical systems of gyrotrons 5-22
5.3.1 Conventional EOS 5-22
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HighFrequencySourcesofCoherentRadiationforFusionPlasmas
5.3.2 EOS of LOG 5-27
5.3.3 Cathodes of MIG for gyrotrons 5-28
5.4 Quasi-optical systems of the gyrotrons 5-30
5.5 Output windows of the gyrotrons 5-35
References 5-37
6 CARM theory and relevant phenomenology 6-1
6.1 Introduction 6-1
6.2 U-FEL, gyrotron, CARM interaction: a common point view 6-5
6.2.1 Small signal theory: FEL versus CARM analytical solution 6-10
6.3 Non-linear regime and saturated power 6-17
6.3.1 The 1D GRAAL code 6-19
6.4 FEL to CARM scaling law 6-20
6.5 Transverse mode selection: operating configuration 6-24
6.6 CARM oscillator and cavity design: numerical simulation 6-28
6.7 Operating mode selection: Q-factor, starting current and cavity length 6-32
6.8 Starting current and energy spread 6-41
References 6-43
7 Plasma heating with coherent FEL-like sources 7-1
7.1 U-FEL and fusion applications 7-1
7.2 Gyrotron for fusion and current status 7-10
7.3 The CARM design for fusion application 7-18
7.3.1 Gun design and e-beam qualities 7-23
7.3.2 The e-beam transport line modeling 7-28
7.4 A hint to the development of future technologies 7-34
7.4.1 RF undulators and wigglers 7-34
References 7-46
Appendices
Appendix A A-1
Appendix B B-1
Appendix C C-1
vii
Preface
This book deals with the scientific and technological aspects associated with those
devices currently exploited for the heating of magnetically confined fusion plasma
with intense electromagnetic waves.
The book consists of two parts; the first dealing with the basics elements of
plasma physics, the second accounts for electromagnetic sources designed as
external plasma heaters. We will discuss particular items, like free electron laser
(FEL) type generators of coherent electromagnetic radiation, designed to provide
the supplementary power necessary to ignite, heat and sustain the plasma. They
cannot, therefore, be separatedfrom the physical aspects of magnetic fusion and of
magnetized plasma, which are initially sketched in the first three chapters.
Before getting into the book plan, we would like to mention that this effort
merges four different expertises, which encompass the physics of undulator FELs,
the physics of gyrotrons, that of cyclotron auto-resonance maser (CARM), and
more generally the physics of charged particles–radiation interaction. The skills of
theauthorsareequallydistributedbetweentheoretical,experimentalandnumerical
competencies, but do not include any long-term experience of direct work on
plasma.
Eventhoughthiscreatedamajorprobleminwritingthebook,itturnedouttobe
a decisive advantage because we have been obliged to study deeply what we had
learned in the past in amateur terms.
We filtered the physics and Tokamak engineering through our own scientific
experiences and the results are those summarized in the first three chapters, which
deal with the physics of fusion plasma, the physics of Tokamaks, the associated
technical issues and some aspects of the additional heating.
The subsequent chapters cover a general introduction to the FEL-like coherent
sources and more specific descriptions of the physics of undulator FELs, gyrotrons
and CARM.
We have placed particular emphasis on the description of the latter device, for
different reasons, including the fact that it was the main topic of our research in
recent years. It is an extremely challenging device, because it requires significant
technological efforts, which go from an extremely demanding power supply, to a
high performing electron gun capable of providing a high quality beam and a
corresponding beam transport system.
The compilation of the book has been conceived in a painful period for the
authors’life.Theyhavelostbelovedpeoplewhohadplayedacentralroleintermsof
affection, support, and presence in their growth, not just professional. Therefore
GiuseppeDattolidedicatesthebooktohismotherAda, EmanueleDiPalmatohis
father Andrea, Svilen Sabchevski to his wife Petia and Ivan Spassovsky to his
parents Rumiana and Pano.
The book comes after years of intensive research work in the field. We had been
assisted by more experienced colleagues.
viii
HighFrequencySourcesofCoherentRadiationforFusionPlasmas
We express our gratitude to Dr A Cardinali and Ing. F Mirizzi for reading and
correcting the first two chapters. Discussions on weak interactions and solar
‘burning’withDrFAlladiohavebeenusefultoclearourmindsofmanydangerous
(wrong) commonplaces.
The understanding of the physics of gyrotrons and CARM has benefitted from
discussions with Professor G Nusinovich who shared with us years of experience in
these fields.
The generous effort in correcting our misconceptions by Professors N Ginzburg,
M Glyavin, N Peskov and A Savilov from IPA-RAS Nizhny Novgorod has been
greatly appreciated.
It is finally a great pleasure to thank the colleagues of the CARM task force at
ENEA Frascati for sharing with us many enlightening discussions on the topics
treated in this book.
Giuseppe Dattoli
Emanuele Di Palma
Svilen Petrov Sabchevski
Ivan Panov Spassovsky
ix
