The limits of traditional magnets.

1. The limits of traditional magnets. The limits of traditional magnets force physicists to use superconducting magnets in LHC experiments

2. Magnetic field, permeability, magnetic induction. • A magnetic field H, passing through a certain material causes magnetic effects in this material. The factor µ, called the permeability, reflects the effect. The result, as felt by a sensor, is the magnetic induction B: B = µ*H. • So, B is the effect on a sensor (charged particle), µ gives the influence of the material, H is the source. CERN HST 2001

3. The magnetic field H • A coil with N windings, length l and current I produces a magnetic field • If l is small, or I is big, H is large. • The coil acts a the source of magnetism CERN HST 2001

4. The permeability µ • This quantity gives an idea of how the material can be magnetized. • Diamagnetic and paramagnetic materials hardly affect magnetic fields at all, so they have a low permeability • For « ferromagnetic » materials µ is a big number • Ferromagnetic (iron) yokes determine the resulting field • quantitatively, • but the shape of the yoke also influences the form of the field CERN HST 2001

5. Magnetic induction B • What a sensor or a charged particle feels is the product of the field caused by the coil, H, and the influence of the material, µ. This is the magnetic induction B. • The Lorentz force needs B. • The force acts perpendicular on the B field. The surface must be very flat and horizontal, to be sure that the quality of the beam remains high CERN HST 2001

6. Special situations • The internal Weiss areas play a keyrole in ferromagnetic materials. The easier these align along the H-field, the bigger µ of the material • If H is very high, more and more Weiss areas align, until saturation is yielded: at this stage no more magnetic dipoles are left in the material to align • In practice, B reaches a maximum value of 2T, increasing H does not help. CERN HST 2001

7. For example: synthesis • The coils are horizontal • The yoke is made of a material with avery high µ value • h (= the distance) is kept very small • The beam feels B, the combination of both. CERN HST 2001

8. Limits • They use concrete to stabilize the form of the ferromagnetic yoke. • For a magnetic field of 0,3 T as in the LEP injection dipole magnet, you need a power of 20 kW per magnet. There are some 500 magnets in LEP, this means a total power only for these magnets, of 10 MW. CERN HST 2001

9. The heat problem • The total resistance of the wire used is 0,08 . The current is500 A. The loss of thermal energy per second isDEth = R * I² * Dt = ........ • There are 500 such magnets so .... CERN HST 2001

10. The cooling problem • They need lots of water to cool the magnet. • This is a loss of energy. • How much water would you need to pump every second through the magnet to cool everything? Suppose that you inject water of 15°C and eject again at 90°C. CERN HST 2001

11. Even worse... • Remember: B = 0,3 T is the magnets mentioned above. • The upper limit of these traditional kinds magnets is 2T. • How much water would you need to cool those magnets? • Don’t forget that the energy to take away ~ I2 ! To have a magnet twice as strong, you would need to take 4 times more heat away. CERN HST 2001

12. The traditional coil. CERN HST 2001

13. Cross section of LEP dipole cooling channels CERN HST 2001