Patent ID: 8467999

Claim:
A method of constructing electrical coils for generating an asymmetric cusp magnetic field within a single crystal furnace, the method comprising: establishing a first mathematical expression of electrical coil heat as: w ⁢ ⁢ 1 = I 2 ⁢ l s ⁢ ρ 0 ⁡ ( 1 + at ) , where I is a current of the coils, l is the total length of the coils, s is the cross-sectional area of the coils, p 0 is the resistivity of the coils, a is a temperature coefficient of resistivity, and t is the temperature of copper pipe walls of the coils; establishing a second mathematical expression of heat transfer at the copper pipe walls as: w ⁢ ⁢ 2 = 0.023 ⁢ λ ⁢ ⁢ A de ⁢ ( Vde v ) 0.8 ⁢ Pr 0.4 ⁢ Δ ⁢ ⁢ t , where de is a characteristic size, V is an average flow velocity of cooling water, Δt is the temperature difference between the copper pipe walls and the cooling water, λis the heat conductivity of the cooling water, A is the total heat transferring area of the copper pipe walls, ν is the kinematic viscosity of the cooling water, and Pr is a Prandtl number; establishing a third mathematical expression of heat absorbed by the cooling water as follows: w 3 =q m c ( t 2 −t 1)· n , where q m is the amount of cooling water flow, c is the specific heat capacity of the cooling water, t2 is the water temperature at a cooling water outlet, t1 is the water temperature at a cooling water inlet, and n is the number of cooling water paths for the copper pipes; determining, with a processor, values for parameters s and l of the coils for which a minimum value of w1 satisfies the relation w1=w2=w 3 , Δt+t2<40 and hf<20, where Δt+t2 is the temperature of the copper pipe walls and hf is the linear loss along the coils; and constructing coils in accordance with the values determined for the parameters s and l.