226 lines
6.6 KiB
Fortran
226 lines
6.6 KiB
Fortran
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!=======================================================================
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!
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MODULE DECAY_RATE
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!
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USE ACCURACY_REAL
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!
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!
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CONTAINS
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!=======================================================================
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!
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SUBROUTINE DECAY_RATE_COEF(X,DR)
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!
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! This subroutine computes the decay rate
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!
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!
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! Input parameters:
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!
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! * X : dimensionless factor --> X = q / (2 * k_F)
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!
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!
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! Output parameters:
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!
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! * DR : decay rate
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!
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 12 Nov 2020
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!
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!
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USE MATERIAL_PROP, ONLY : DMN,RS
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USE EXT_FIELDS, ONLY : T
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USE LF_VALUES, ONLY : GQ_TYPE,IQ_TYPE
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USE SF_VALUES, ONLY : SQ_TYPE
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!
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USE DAMPING_VALUES, ONLY : DR_TYPE
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!
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IMPLICIT NONE
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!
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REAL (WP), INTENT(IN) :: X
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REAL (WP), INTENT(OUT) :: DR
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!
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IF(DMN == '3D') THEN !
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CALL DECAY_RATE_3D(X,T,RS,DR_TYPE,SQ_TYPE,GQ_TYPE, & !
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IQ_TYPE,DR) !
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ELSE IF(DMN == '2D') THEN !
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CONTINUE ! not implemented yet
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ELSE IF(DMN == '1D') THEN !
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CONTINUE ! not implemented yet
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END IF !
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!
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END SUBROUTINE DECAY_RATE_COEF
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!
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!=======================================================================
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!
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SUBROUTINE DECAY_RATE_3D(X,T,RS,DR_TYPE,SQ_TYPE,GQ_TYPE, &
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IQ_TYPE,DR)
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!
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! This subroutine computes the plasmon decay rate
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!
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!
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! Input parameters:
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!
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! * X : dimensionless factor --> X = q / (2 * k_F)
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! * T : temperature (in SI)
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * DR_TYPE : type of decay rate
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! DR_TYPE = 'UTIC' --> Utsumi-Ichimaru approximation
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! DR_TYPE = 'VLAS' --> Vlasov approximation
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! * SQ_TYPE : structure factor approximation (3D)
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! * GQ_TYPE : local-field correction type (3D)
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! * IQ_TYPE : type of approximation for I(q)
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!
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! Output parameters:
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!
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! * DR : decay rate
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!
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 11 Jun 2020
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!
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!
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!
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IMPLICIT NONE
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!
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CHARACTER (LEN = 4) :: DR_TYPE,GQ_TYPE
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CHARACTER (LEN = 3) :: SQ_TYPE,IQ_TYPE
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!
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REAL (WP) :: X,T,RS
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REAL (WP) :: DR
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!
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IF(DR_TYPE == 'UTIC') THEN !
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DR=UTIC_DR_3D(X,RS,T,SQ_TYPE,GQ_TYPE,IQ_TYPE) !
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ELSE IF(DR_TYPE == 'VLAS') THEN !
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DR=VLAS_DR_3D(X,T,RS) !
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END IF !
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!
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END SUBROUTINE DECAY_RATE_3D
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!
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!=======================================================================
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!
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FUNCTION UTIC_DR_3D(X,RS,T,SQ_TYPE,GQ_TYPE,IQ_TYPE)
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!
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! This function computes Utsumi-Ichimaru approximation for
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! the decay rate in the 3D case
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!
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! Reference: (1) K. Utsumi and S. Ichimaru,
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! Phys. Rev. B 22, 1522-1533 (1980)
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!
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!
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! Input parameters:
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!
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! * X : dimensionless factor --> X = q / (2 * k_F)
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : temperature (in SI)
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! * SQ_TYPE : structure factor approximation (3D)
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! * GQ_TYPE : local-field correction type (3D)
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! * IQ_TYPE : type of approximation for I(q)
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!
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! Output parameters:
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!
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! * UTIC_DR : decay rate
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!
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! Author : D. Sébilleau
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!
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! Last modified : 3 Dec 2020
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!
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!
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USE REAL_NUMBERS, ONLY : HALF
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USE CONSTANTS_P1, ONLY : H_BAR
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USE UTIC_PARAMETERS, ONLY : UTIC_PARAM
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USE RELAXATION_TIME_STATIC, ONLY : UTIC_RT_3D
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USE PLASMON_ENE_SI
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!
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IMPLICIT NONE
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!
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CHARACTER (LEN = 4) :: GQ_TYPE
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CHARACTER (LEN = 3) :: SQ_TYPE,IQ_TYPE
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!
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REAL (WP), INTENT(IN) :: X,RS,T
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REAL (WP) :: UTIC_DR_3D
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!
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REAL (WP) :: OMP
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REAL (WP) :: TAU_Q,OMQ,OM0
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!
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REAL (WP) :: EXP
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!
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OMP = ENE_P_SI / H_BAR ! omega_p in SI
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!
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! Computing the Utsumi-Ichimaru parameters OMEGA(q) and OMEGA(0)
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!
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CALL UTIC_PARAM(X,RS,T,OMQ,OM0) !
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!
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! Computing the relaxation time TAU_Q
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!
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TAU_Q = UTIC_RT_3D(X,RS,T,SQ_TYPE,GQ_TYPE) !
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!
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UTIC_DR_3D = - HALF * EXP(- HALF * (OMP / OM0)**2) / TAU_Q ! ref. 1 eq. (5.13)
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!
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END FUNCTION UTIC_DR_3D
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!
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!=======================================================================
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!
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FUNCTION VLAS_DR_3D(X,RS,T)
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!
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! This function computes Vlasov approximation for
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! the decay rate in the 3D case
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!
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! Reference: (1) S. Ichimaru, "Statistical Plasma Physics - Vol1",
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! CRC Press (2004)
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!
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!
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! Input parameters:
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!
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! * X : dimensionless factor --> X = q / (2 * k_F)
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : temperature (in SI)
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!
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! Output parameters:
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!
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! * VLAS_DR : relaxation time in seconds
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!
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! Author : D. Sébilleau
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!
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! Last modified : 11 Jun 2020
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!
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!
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USE REAL_NUMBERS, ONLY : TWO,THREE,HALF
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USE CONSTANTS_P1, ONLY : H_BAR,M_E,K_B
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USE FERMI_SI, ONLY : KF_SI
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USE PI_ETC, ONLY : PI
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USE SCREENING_VEC, ONLY : DEBYE_VECTOR
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USE PLASMON_ENE_SI
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!
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IMPLICIT NONE
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!
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REAL (WP) :: X,RS,T
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REAL (WP) :: VLAS_DR_3D
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REAL (WP) :: Q_SI,KD_SI,OQ2,AA
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!
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REAL (WP) :: DSQRT,DEXP
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!
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Q_SI=TWO*X*KF_SI ! q
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!
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! Computing the Debye screening vector
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!
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CALL DEBYE_VECTOR('3D',T,RS,KD_SI) !
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!
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! Computing the square of the Vlasov plasmon dispersion
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!
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OQ2=ENE_P_SI*ENE_P_SI + THREE*K_B*T*Q_SI*Q_SI/M_E ! ref. 1 eq. (4.30)
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!
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AA=HALF*M_E*OQ2/(Q_SI*Q_SI*K_B*T) !
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!
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VLAS_DR_3D=DSQRT(0.125E0_WP*PI)*ENE_P_SI*(KD_SI/Q_SI)**3 * & ! ref. 1 eq. (4.31)
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DEXP(-AA) / H_BAR !
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!
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END FUNCTION VLAS_DR_3D
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!
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END MODULE DECAY_RATE
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