Elements of Superconductivity and Physics of High Field Magnets
A.Y. 2024/2025
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 can be attended as a single course.
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
- Distribuited 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
- Distribuited 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. Presence at lessons suggested.
Teaching Resources
Course book given by the teacher 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.
Educational website(s)
Professor(s)
Reception:
Monday from h. 10 to h. 12
LASA lab. (or Physics Department, by appointment)