belfem::material::JcFunctionModifiedKim Class Reference

Modified Kim model for critical current density. More...

#include <cl_JcFunction_ModifiedKim.hpp>

Inheritance diagram for belfem::material::JcFunctionModifiedKim:

Collaboration diagram for belfem::material::JcFunctionModifiedKim:

Public Member Functions
	JcFunctionModifiedKim (const real jc0, const real B0, const real k2, const real alpha)
	Constructor for modified Kim model.
	~JcFunctionModifiedKim () override=default
real	eval (const real normB, const real angle) const override
	Evaluate Jc at given field and angle.
real	deval_dB (const real normB, const real angle, const real T) const override
	Derivative of eval with respect to the field magnitude.
Public Member Functions inherited from belfem::material::JcFunction
	JcFunction ()=default
virtual	~JcFunction ()=default
bool	depends_on (const JcParameter aParameter) const
virtual real	min_value () const
	Smallest value this function can return, when known.
bool	is_constant () const
virtual real	eval (const real normB, const real angle, const real T) const
	Evaluate with full temperature, field, and angle dependence.
virtual real	deval_dbeta (const real normB, const real angle, const real T) const
	Derivative of eval with respect to the field angle.
virtual real	deval_dT (const real normB, const real angle, const real T) const
	Derivative of eval with respect to temperature.

Additional Inherited Members
Protected Member Functions inherited from belfem::material::JcFunction
void	set_dependency (const JcParameter aParameter)
	Mark function as depending on a parameter.
Protected Attributes inherited from belfem::material::JcFunction
JcDependency	mDependency

Detailed Description

Modified Kim model for critical current density.

Implements an analytical model for Jc(B, angle) based on the modified Kim-Anderson relation with angular dependence.

Model equation:

Jc(B,θ) = Jc0 / [1 + √(k²·sin²(θ) + cos²(θ)) · B/B0]^α

where:

• Jc0: Critical current density at zero field [A/m²]
• B0: Characteristic field scale [T]
• k: Anisotropy parameter (k < 1 means field parallel to the c-axis / surface normal reduces Jc more than in-plane field; k = 1 is isotropic)
• α: Exponent controlling field dependence (typically 0.5-1.0)
• θ: Angle between surface normal and magnetic field [rad]

Dependencies: normB, angleNxB

Reference:

• 10.1088/0953-2048/24/6/065024 (Ekin scaling law with angular correction)

Usage:

JcFunction* jc = new JcFunctionModifiedKim(
    1e9,   // Jc0 = 1 GA/m² at zero field
    5.0,   // B0 = 5 T characteristic field
    0.5,   // k² = 0.5 anisotropy
    2.0    // α = 2.0 exponent
);
material->set_jc_function(jc);  // Material takes ownership

Constructor & Destructor Documentation

JcFunctionModifiedKim()

belfem::material::JcFunctionModifiedKim::JcFunctionModifiedKim ( const real jc0, const real B0, const real k2, const real alpha )

inline

Constructor for modified Kim model.

Parameters

jc0	Critical current density at zero field [A/m²]
B0	Characteristic field scale [T]
k2	Anisotropy parameter k² (dimensionless, typically 0.1-10)
alpha	Field dependence exponent α (typically 0.5-2.0)

Creates a modified Kim function with angular dependence. The model is valid for normB > 0 and all angles.

Reference: 10.1088/0953-2048/24/6/065024

~JcFunctionModifiedKim()

belfem::material::JcFunctionModifiedKim::~JcFunctionModifiedKim ( )

overridedefault

Member Function Documentation

deval_dB()

real belfem::material::JcFunctionModifiedKim::deval_dB ( const real normB, const real angle, const real T ) const

inlineoverridevirtual

Derivative of eval with respect to the field magnitude.

Parameters

normB	Magnetic field magnitude [T]
angle	Angle between surface normal and field [rad]
T	Temperature [K], unused: the law has no temperature dependence

Returns

d(Jc)/d|B| [A/m²/T]

With s = √(k²·sin²(θ) + cos²(θ)): dJc/dB = -α · Jc · s / ( B0 + s·B )

Exact for the law in eval().

Reimplemented from belfem::material::JcFunction.

eval()

real belfem::material::JcFunctionModifiedKim::eval ( const real normB, const real angle ) const

inlineoverridevirtual

Evaluate Jc at given field and angle.

Parameters

normB	Magnetic field magnitude [T]
angle	Angle between surface normal and field [rad]

Returns

Critical current density Jc [A/m²]

Evaluates the modified Kim model: Jc = Jc0 / [1 + √(k²·sin²(θ) + cos²(θ)) · B/B0]^α

The law is even in θ because it uses only cos² and sin². An unfolded angle θ ∈ [0, π] gives the same result as a folded [0, π/2] input, so this law needs no internal fold.

Reimplemented from belfem::material::JcFunction.

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The documentation for this class was generated from the following file:

• src/physics/materials/cl_JcFunction_ModifiedKim.hpp