 # Magnet Safety

MAGS Model

Severe thermal problems up to conductor melting and arcing are possible for superconducting coils when the superconducting state is lost

Superconductivity of NbTi or Nb3Sn is a function of magnetic field, current density, temperature and strain. The latter is determined by mechanical analysis or measurement and used as an input parameter here. For the other items and calculations of consequences of loss of superconductivity numerical models are available:

### Magnetic field

Single coils or complete coil systems as for a tokamak can be considered.

• Input is: geometry, current and number of turns
• Output is: inductance, force and magnetic field

### Electrical circuit

The circuit can be composed from resistances, inductances, capacities and switches.

• Input is: inductance, resistance, initial conditions
• Output is: voltage, current in conductor, induced current in e.g. radial plate and resulting heat source

### Electric arc

Voltage-current characteristic for arcs.

• Input is: current
• Output is: resistance, heat source

Area under development: Model for arcs at power supply lines (busbars) of the coils.

### Short

Three-dimensional current in winding pack after insulation failure.

• Input is: voltage, temperature, current source
• Output is: voltage, heat sources, total resistance

### Thermal analysis of winding pack

Three dimensional heat conduction in winding pack.

• Input is: heat sources/sinks, boundary conditions to coil case
• Output is: temperature, heat fluxes exchanged with coil case

### Forced flow Helium

One dimensional mass, momentum and energy balance.

• Input is: temperature of structure, boundary pressure and temperature for channels
• Output is: heat sink, mass fluxes at inlet and outlet of channels

Area under development: helium thermal decoupling effects in conductor cross section, buoyancy.

### Boundary conditions

Mass momentum and energy balance of helium piping outside of coil.

• Input is: fluxes at inlet and outlet of channels, conditions in reservoirs
• Output is: pressure and temperature for channels

### Eddy currents in conductor

• Input is: local magnetic field change rate
• Output is: local heat source

### Quench detection

• Input is: strain, temperature, magnetic field, current
• Output is: local heat source, resistance

### Coil case

• Three-dimensional heat conduction in coil case.
• Input is: heat fluxes exchanged with winding pack, boundary conditions of cryostat
• Output is: boundary conditions for winding pack, heat fluxes exchanged with cryostat

### Cryostat

Mass momentum and energy balance for connected volumes, and condensation.

• Input is: state in reservoirs and connecting pipes, heat flux on volume surfaces, heat fluxes exchanged with cryostat
• Output is: boundary conditions for coil case, boundary conditions for cryostat wall

Area under development: Condensation at cryogenic surfaces.

### Wall

One-dimensional heat balance for walls bounding the volumes.

• Input is: boundary conditions for wall
• Output is: heat flux on volume surfaces

Each of these subtasks is evaluated by a corresponding MAGS module. The MAGS modules are called one after the other at a certain time step. They work together by using and updating the same database

Applications