Applied Superconductivity
A.Y. 2019/2020
Learning objectives
The course aims at providing competences on the application of superconductivity to produce of high magnetic fields for physics research and particularly for particle accelerators. The first part of the course recalls aspects on classic thermodynamics useful to the basic comprehension of superconductivity and to the principles to reach low temperatures. In the second part a description of the current transport properties in superconductors is given. In the last part the problems concerning the design and construction in superconducting magnets are described.
Expected learning outcomes
At the end of the course the student will have acquired the following competences:
1. knowledge of working principles of systems to reach the low temperature, with ability to evaluate limits and working operativity.
2. Properties and macroscopic phenomenology of superconductor of I and II specie.
3. Property of current transport in superconductor II specie and limits.
4. Instability in superconductors.
5. Losses in superconductors
6. Critical aspects and design element of high field superconducting magnets for particle accelerators: aspects of electromagnetic, mechanical, thermal and quench protection design.
1. knowledge of working principles of systems to reach the low temperature, with ability to evaluate limits and working operativity.
2. Properties and macroscopic phenomenology of superconductor of I and II specie.
3. Property of current transport in superconductor II specie and limits.
4. Instability in superconductors.
5. Losses in superconductors
6. Critical aspects and design element of high field superconducting magnets for particle accelerators: aspects of electromagnetic, mechanical, thermal and quench protection design.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
1. Thermodynamics and Cryogenics (9 hours)
Thermodynamics states in P-V diagram
First principle of thermodynamics
Work for magnetization and de-magnetization
Second principle of thermodynamics
Entropy and state function
Clausius inequality
Entropy properties
Van Der Waals gas equation
Irreversible expansion in Van Der Waals
Isoenthalèic expansion in ideal gas, Van Der Waals gas and real gas
Rappresentation of thermal cycles in diagram T-S
Diagram T-S for ideal and real gases
Principles of liquifier (cascade liquefier, Linde cycle, Stirling cycle)
Adiabatic demagnetization
Third principle of thermodynamics
Thermodynamics potentials (free energy of Helmholtz, Gibbs potential)
Phase transition of I and II second order
Gibbs potential applied to superconductor transitions.
Entropic states in a material in normal and superconducting states.
Mixed state in a superconductor for the de-magnetization field
2. Foundaments of superconductivity, first and second type of superconductors (10 hours)
Meissner-Ochsenfeld effect
Critical current in II type superconductor
London model
Foundaments of BCS
Wave phase in cooper couples
The fluxoid
The superconductivity of II type and fluxoid lattice
Superficial energy for coherence length
Critical fields in II type superconductors
Critical current in II types superconductors
Flux flow resistance
3 Critical state model (Bean model) e and application in II type superconductors (8 hours)
Transport current and pinning force
Critical state model (Bean model)
Adiabatic stabilityc (unidimensional model)
Magnetization curve in a superconductors
4. Superconducting Magnets (15 hours)
Topology of magnets (solenoid, toroid, dipole and quadrupole for particle accelerator)
Dipole and quadrupole normal conducting iron dominated
Dipole and quadrupole current dominated
Field analysis with complex formalism.
Cos-m-theta magnets: internal and external fields
Forces in solenoids and analytic methods for evaluation
Hoop stress in solenoid
Foces in dipole cos-theta (superficial current approximation)
Load line in a magnet, working point training in superconducting magnets
Ditribuited and puntual disturbs in superconducting magnets
Minimum Propagation Zone evaluation in one dimension
Protection of a superconducting magnet
Evaluation of maximum voltage during a quench
Hot-spot-temperature evaluation in a quench
Optimization of conductor for hot spot temperature.
Thermodynamics states in P-V diagram
First principle of thermodynamics
Work for magnetization and de-magnetization
Second principle of thermodynamics
Entropy and state function
Clausius inequality
Entropy properties
Van Der Waals gas equation
Irreversible expansion in Van Der Waals
Isoenthalèic expansion in ideal gas, Van Der Waals gas and real gas
Rappresentation of thermal cycles in diagram T-S
Diagram T-S for ideal and real gases
Principles of liquifier (cascade liquefier, Linde cycle, Stirling cycle)
Adiabatic demagnetization
Third principle of thermodynamics
Thermodynamics potentials (free energy of Helmholtz, Gibbs potential)
Phase transition of I and II second order
Gibbs potential applied to superconductor transitions.
Entropic states in a material in normal and superconducting states.
Mixed state in a superconductor for the de-magnetization field
2. Foundaments of superconductivity, first and second type of superconductors (10 hours)
Meissner-Ochsenfeld effect
Critical current in II type superconductor
London model
Foundaments of BCS
Wave phase in cooper couples
The fluxoid
The superconductivity of II type and fluxoid lattice
Superficial energy for coherence length
Critical fields in II type superconductors
Critical current in II types superconductors
Flux flow resistance
3 Critical state model (Bean model) e and application in II type superconductors (8 hours)
Transport current and pinning force
Critical state model (Bean model)
Adiabatic stabilityc (unidimensional model)
Magnetization curve in a superconductors
4. Superconducting Magnets (15 hours)
Topology of magnets (solenoid, toroid, dipole and quadrupole for particle accelerator)
Dipole and quadrupole normal conducting iron dominated
Dipole and quadrupole current dominated
Field analysis with complex formalism.
Cos-m-theta magnets: internal and external fields
Forces in solenoids and analytic methods for evaluation
Hoop stress in solenoid
Foces in dipole cos-theta (superficial current approximation)
Load line in a magnet, working point training in superconducting magnets
Ditribuited and puntual disturbs in superconducting magnets
Minimum Propagation Zone evaluation in one dimension
Protection of a superconducting magnet
Evaluation of maximum voltage during a quench
Hot-spot-temperature evaluation in a quench
Optimization of conductor for hot spot temperature.
Prerequisites for admission
Electromagnetism. Foundament of quantum physics
Teaching methods
Frontal lessons and calculus in dashboard
Teaching Resources
Massimo Sorbi, Superconduttività Applicata, Dispensa del corso (delivered during lessons)
Assessment methods and Criteria
The exam consists in an oral colloquium where some of the topics of the course are requested to be presented. The student has to be able to evaluate qualitatively and quantitatively the topics which he/she presents. The colloquium may be 45 min long.
FIS/01 - EXPERIMENTAL PHYSICS - University credits: 6
Lessons: 42 hours
Professor:
Sorbi Massimo
Shifts:
-
Professor:
Sorbi MassimoProfessor(s)
Reception:
Monday from h. 10 to h. 12
LASA lab. (or Physics Department, by appointment)