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
	Destructor.
real	eval (const real normB, const real angle) const override
	Evaluate Jc at given field and angle.
Public Member Functions inherited from belfem::material::JcFunction
	JcFunction ()=default
	Default constructor.
virtual	~JcFunction ()=default
	Virtual destructor.
bool	depends_on (const JcParameter aParameter) const
	Check if function depends on a parameter.
virtual real	min_value () const
	Smallest value this function can return, when known.
bool	is_constant () const
	Check if function is constant (no dependencies).
virtual real	eval (const real normB, const real angle, const real T) const
	Evaluate with full temperature, field, and angle dependence.
virtual real	deval_dB (const real normB, const real angle, const real T) const
	Derivative of eval with respect to the field magnitude.
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

Destructor.

Member Function Documentation

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

Even in θ by construction (cos², sin² only), so the unfolded angle θ ∈ [0, π] delivered since 2026-08-16 evaluates identically to the historical folded [0, π/2] input — this law needs no fold of its own.

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