analytical_functions.f90

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MODULE analytical_functions

  use itm_types
  use itm_constants
  IMPLICIT NONE

CONTAINS



!==============================================================
! +++ MAGNETIC GEOMETRY   
  REAL(R8) FUNCTION arho(I,NRHO)
    INTEGER , INTENT(IN)  ::i,nrho
    arho=1.0_r8/(nrho-1)*(i-1)
  END FUNCTION arho

  REAL(R8) FUNCTION avpr(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    avpr=x
  END FUNCTION avpr

  REAL(R8) FUNCTION dtavpr(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    dtavpr=0.0_r8
  END FUNCTION dtavpr

  REAL(R8) FUNCTION davpr(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    davpr=1.0_r8
  END FUNCTION davpr

  REAL(R8) FUNCTION ag1(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    ag1=1.
  END FUNCTION ag1

  REAL(R8) FUNCTION dag1(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    dag1=0.0_r8
  END FUNCTION dag1

  REAL(R8) FUNCTION dtag1(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    dtag1=0.0_r8
  END FUNCTION dtag1

  REAL(R8) FUNCTION ag2(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    ag2=1.0_r8
  END FUNCTION ag2

  REAL(R8) FUNCTION dag2(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    dag2=0.0_r8
  END FUNCTION dag2

  REAL(R8) FUNCTION dtag2(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    dtag2=0.0_r8
  END FUNCTION dtag2

  REAL(R8) FUNCTION ag3(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    ag3=1.0_r8
  END FUNCTION ag3

  REAL(R8) FUNCTION dag3(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    dag3=0.0_r8
  END FUNCTION dag3

  REAL(R8) FUNCTION afdia(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    afdia=1.0_r8+x
  END FUNCTION afdia

  REAL(R8) FUNCTION dafdia(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    dafdia=1.0_r8
  END FUNCTION dafdia

  REAL(R8) FUNCTION abt(T)
    REAL(R8) ,INTENT(IN)   :: t
    abt=1.0_r8
  END FUNCTION abt

  REAL(R8) FUNCTION dtabt(T)
    REAL(R8) ,INTENT(IN)   :: t
    dtabt=0.0_r8
  END FUNCTION dtabt




! +++ ANALYTICAL PLASMA PROFILES:
  REAL(R8) FUNCTION apsi(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    apsi=x**2*(1+.2_r8*sin(2*itm_pi*t))
  END FUNCTION apsi

  REAL(R8) FUNCTION dtapsi(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    dtapsi=x**2*.2_r8*cos(2.0_r8*itm_pi*t)*2.0_r8*itm_pi
  END FUNCTION dtapsi

  REAL(R8) FUNCTION dapsi(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    dapsi=2.0_r8*x*(1+.2_r8*sin(2*itm_pi*t))
  END FUNCTION dapsi

  REAL(R8) FUNCTION ddapsi(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    ddapsi=2.0_r8*(1+.2_r8*sin(2*itm_pi*t))
  END FUNCTION ddapsi

  REAL(R8) FUNCTION ani(IION,X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    INTEGER, INTENT (IN)   :: iion
    ani=(1.e19_r8*(1.0_r8-x**2)+1.e18_r8)*(1+.2_r8*sin(2*itm_pi*t))
  END FUNCTION ani

  REAL(R8) FUNCTION dani(IION,X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    INTEGER, INTENT (IN)   :: iion
    dani=-x*1.e19_r8*2.0_r8*(1+.2_r8*sin(2*itm_pi*t))
  END FUNCTION dani

  REAL(R8) FUNCTION ddani(IION,X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    INTEGER, INTENT (IN)   :: iion
    ddani=-1.e19_r8*2.0_r8*(1+.2_r8*sin(2*itm_pi*t))
  END FUNCTION ddani

  REAL(R8) FUNCTION dtani(IION,X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    INTEGER, INTENT (IN)   :: iion
    dtani=(1.e19_r8*(1.0_r8-x**2)+1.e18_r8)*.2_r8*cos(2*itm_pi*t)*2.0_r8*itm_pi
  END FUNCTION dtani

  REAL(R8) FUNCTION ati(IION,X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    INTEGER, INTENT(IN )   :: iion
    ati=(1.e6_r8*(1.0_r8-x**2)+1.e2_r8)*(1+.2_r8*sin(2*itm_pi*t))
  END FUNCTION ati

  REAL(R8) FUNCTION dtati(IION,X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    INTEGER, INTENT(IN )   :: iion
    dtati=(1.e6_r8*(1.0_r8-x**2)+1.e2_r8)*.2_r8*cos(2*itm_pi*t)*2.0_r8*itm_pi
  END FUNCTION dtati

  REAL(R8) FUNCTION dati(IION,X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    INTEGER, INTENT(IN )   :: iion
    dati=-2.0_r8*x*1.e6_r8*(1+.2_r8*sin(2*itm_pi*t))
  END FUNCTION dati

  REAL(R8) FUNCTION ddati(IION,X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    INTEGER, INTENT(IN )   :: iion
    ddati=-2.0_r8*1.e6_r8*(1+.2_r8*sin(2*itm_pi*t))
  END FUNCTION ddati

  REAL(R8) FUNCTION ate(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    ate=(1.2e6_r8*(1.0_r8-x**2)+1.e2_r8)*(1+.2_r8*sin(2*itm_pi*t))
  END FUNCTION ate

  REAL(R8) FUNCTION date(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    date=-2.0_r8*x*1.2e6_r8*(1+.2_r8*sin(2*itm_pi*t))
  END FUNCTION date

  REAL(R8) FUNCTION ddate(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    ddate=-2.0_r8*1.2e6_r8*(1+.2_r8*sin(2*itm_pi*t))
  END FUNCTION ddate

  REAL(R8) FUNCTION dtate(X,T)
    REAL(R8) ,INTENT(IN)   :: x,t
    dtate=(1.2e6_r8*(1.0_r8-x**2)+1.e2_r8)*.2_r8*cos(2*itm_pi*t)*2.0_r8*itm_pi
  END FUNCTION dtate

  REAL(R8) FUNCTION avtor(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    avtor=1.e0_r8 +x**2*(1.0_r8+0.2_r8*sin(2.0_r8*itm_pi*t))
  END FUNCTION avtor

  REAL(R8) FUNCTION davtor(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    davtor=2.0_r8*x*(1.0_r8+0.2_r8*sin(2.0_r8*itm_pi*t))   
  END FUNCTION davtor

  REAL(R8) FUNCTION ddavtor(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    ddavtor=2.0_r8*(1.0_r8+0.2_r8*sin(2.0_r8*itm_pi*t))    
  END FUNCTION ddavtor

  REAL(R8) FUNCTION dtavtor(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    dtavtor=x**2*0.2_r8*cos(2.0_r8*itm_pi*t)*2.0_r8*itm_pi
  END FUNCTION dtavtor




! +++ TRANSPORT:

  REAL(R8) FUNCTION aconvtor(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    aconvtor=0.05_r8*x
  END FUNCTION aconvtor

  REAL(R8) FUNCTION daconvtor(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    daconvtor=0.05_r8
  END FUNCTION daconvtor

  REAL(R8) FUNCTION advtor(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    advtor=0.1_r8*x
  END FUNCTION advtor

  REAL(R8) FUNCTION dadvtor(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    dadvtor=0.1_r8
  END FUNCTION dadvtor

  REAL(R8) FUNCTION avti(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    avti=0.05_r8*x
  END FUNCTION avti

  REAL(R8) FUNCTION davti(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    davti=0.05_r8
  END FUNCTION davti

  REAL(R8) FUNCTION akappae(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    akappae=0.2_r8
  END FUNCTION akappae

  REAL(R8) FUNCTION dakappae(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    dakappae=0.0_r8
  END FUNCTION dakappae

  REAL(R8) FUNCTION av(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    av=0.00_r8
  END FUNCTION av

  REAL(R8) FUNCTION dav(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    dav=0.0_r8
  END FUNCTION dav

  REAL(R8) FUNCTION ad(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    ad=0.04_r8
  END FUNCTION ad

  REAL(R8) FUNCTION dad(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    dad=0.0_r8
  END FUNCTION dad

  REAL(R8) FUNCTION akate(X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    akate=0.2_r8
  END FUNCTION akate

  REAL(R8) FUNCTION dakate(X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    dakate=0.0_r8
  END FUNCTION dakate

  REAL(R8) FUNCTION avte(X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    avte=0.0_r8
  END FUNCTION avte

  REAL(R8) FUNCTION davte(X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    davte=0.0_r8
  END FUNCTION davte


  REAL(R8) FUNCTION asigma(X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    asigma=1.0_r8
  END FUNCTION asigma




! +++ SOURCES:

  REAL(R8) FUNCTION acurr_imp(X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    acurr_imp=0.0_r8
  END FUNCTION acurr_imp


  REAL(R8) FUNCTION aui_imp(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    aui_imp=0.0_r8
  END FUNCTION aui_imp

  REAL(R8) FUNCTION aqi_imp(IION,X,T)
    REAL(R8) ,INTENT(IN)  :: x,t
    INTEGER, INTENT (IN)  :: iion
    aqi_imp=0.0_r8
  END FUNCTION aqi_imp

  REAL (R8) FUNCTION asi_imp(IION,X,T)
    REAL (R8) ,INTENT(IN)  ::x,t
    INTEGER , INTENT(IN)   :: iion
    asi_imp=0.0_r8
  END FUNCTION asi_imp

  REAL (R8) FUNCTION aqe_imp(X,T)
    REAL (R8) ,INTENT(IN)  :: x,t
    aqe_imp=0.0_r8
  END FUNCTION aqe_imp



!==============================================================
!==============================================================


END MODULE analytical_functions