Magnetic stiffness

The magnetic stiffness describes the property of a fast charged particle to allow its orbit to be more or less 'bent' by magnetic fields . It is obtained by equating the Lorentz force and the centripetal force : ${\displaystyle B\cdot \rho }$

${\displaystyle B\cdot \rho ={\frac {\gamma \cdot m\cdot v}{q}}}$,

in which

• ${\displaystyle B}$the strength of the magnetic field
• ${\displaystyle \rho }$the radius of curvature of the particle trajectory
• ${\displaystyle \gamma }$the Lorentz factor
• ${\displaystyle v}$ the speed of the particle
• ${\displaystyle m}$ its mass
• ${\displaystyle q}$ the charge.

The magnetic stiffness is usually given in Tm ( Tesla times meter ).

This value is important for particle accelerators , especially synchrotrons and cyclotrons : the higher the energy , the greater the speed and the Lorentz factor and thus the magnetic stiffness. However, since the strength of the magnetic field can not be increased at will, the radius of the system must be selected to be correspondingly large. The strongest dipole magnets of today's synchrotrons have a maximum field strength of 8.6 T (see LHC ).