diff --git a/include/picongpu/algorithms/AssignedTrilinearInterpolation.hpp b/include/picongpu/algorithms/AssignedTrilinearInterpolation.hpp
index f002548900..c4d3a61dd1 100644
--- a/include/picongpu/algorithms/AssignedTrilinearInterpolation.hpp
+++ b/include/picongpu/algorithms/AssignedTrilinearInterpolation.hpp
@@ -20,7 +20,6 @@
 #pragma once
 
 #include <pmacc/attribute/unroll.hpp>
-#include <pmacc/result_of_Functor.hpp>
 #include <pmacc/types.hpp>
 
 #include <type_traits>
@@ -54,9 +53,11 @@ namespace picongpu
          *
          * @tparam T_begin lower margin for interpolation
          * @tparam T_end upper margin for interpolation
+         * @tparam T_FieldAccessorFunctor type of the field access functor supporting a initializer list of simdDim
+         *                                indices
          * @tparam T_AssignmentFunction type of shape functors
          *
-         * @param cursor cursor pointing to the field
+         * @param fieldAccess field access method pointing to the particle located cell
          * @param shapeFunctors Array with d shape functors, where d is the dimensionality of the field represented by
          *                      cursor. The shape functor must have the interface to call
          *                      `operator()(relative_grid_point)` and return the assignment value for the given grid
@@ -67,14 +68,14 @@ namespace picongpu
          *
          * @{
          */
-        template<int T_begin, int T_end, typename T_Cursor, typename T_AssignmentFunction>
+        template<int T_begin, int T_end, typename T_FieldAccessorFunctor, typename T_AssignmentFunction>
         HDINLINE static auto interpolate(
-            const T_Cursor& cursor,
-            const pmacc::memory::Array<T_AssignmentFunction, 3>& shapeFunctors)
+            T_FieldAccessorFunctor const& fieldAccess,
+            pmacc::memory::Array<T_AssignmentFunction, 3> const& shapeFunctors)
         {
             [[maybe_unused]] constexpr auto iterations = T_end - T_begin + 1;
 
-            using type = decltype(*cursor(0, 0, 0) * shapeFunctors[0](0));
+            using type = decltype(fieldAccess({0, 0, 0}) * shapeFunctors[0](0));
 
             /* The implementation assumes that x is the fastest moving index to iterate over contiguous memory
              * e.g. a row, to optimize memory fetch operations.
@@ -93,7 +94,7 @@ namespace picongpu
                         /* a form factor is the "amount of particle" that is affected by this cell
                          * so we have to sum over: cell_value * form_factor
                          */
-                        result_x += *cursor(x, y, z) * shapeFunctors[0](x);
+                        result_x += fieldAccess({x, y, z}) * shapeFunctors[0](x);
 
                     result_y += result_x * shapeFunctors[1](y);
                 }
@@ -103,14 +104,14 @@ namespace picongpu
         }
 
         /** Implementation for 2D position*/
-        template<int T_begin, int T_end, class T_Cursor, class T_AssignmentFunction>
+        template<int T_begin, int T_end, class T_FieldAccessorFunctor, class T_AssignmentFunction>
         HDINLINE static auto interpolate(
-            T_Cursor const& cursor,
+            T_FieldAccessorFunctor const& fieldAccess,
             const pmacc::memory::Array<T_AssignmentFunction, 2>& shapeFunctors)
         {
             [[maybe_unused]] constexpr int iterations = T_end - T_begin + 1;
 
-            using type = decltype(*cursor(0, 0) * shapeFunctors[0](0));
+            using type = decltype(fieldAccess({0, 0}) * shapeFunctors[0](0));
             /* The implementation assumes that x is the fastest moving index to iterate over contiguous memory
              * e.g. a row, to optimize memory fetch operations.
              */
@@ -123,7 +124,7 @@ namespace picongpu
                 for(int x = T_begin; x <= T_end; ++x)
                     // a form factor is the "amount of particle" that is affected by this cell
                     // so we have to sum over: cell_value * form_factor
-                    result_x += *cursor(x, y) * shapeFunctors[0](x);
+                    result_x += fieldAccess({x, y}) * shapeFunctors[0](x);
 
                 result_y += result_x * shapeFunctors[1](y);
             }
diff --git a/include/picongpu/algorithms/FieldToParticleInterpolation.hpp b/include/picongpu/algorithms/FieldToParticleInterpolation.hpp
index 95ae030ae5..2015be788f 100644
--- a/include/picongpu/algorithms/FieldToParticleInterpolation.hpp
+++ b/include/picongpu/algorithms/FieldToParticleInterpolation.hpp
@@ -26,8 +26,6 @@
 #include "picongpu/particles/shapes.hpp"
 
 #include <pmacc/attribute/unroll.hpp>
-#include <pmacc/cuSTL/algorithm/functor/GetComponent.hpp>
-#include <pmacc/cuSTL/cursor/FunctorCursor.hpp>
 #include <pmacc/math/Vector.hpp>
 
 namespace picongpu
@@ -95,28 +93,31 @@ namespace picongpu
             return result;
         };
 
-        template<class Cursor, class VecVector>
-        HDINLINE typename Cursor::ValueType operator()(
-            Cursor field,
-            const floatD_X& particlePos,
-            const VecVector& fieldPos)
+        template<class T_FieldDataBox, class VecVector>
+        HDINLINE auto operator()(T_FieldDataBox const& field, const floatD_X& particlePos, const VecVector& fieldPos)
         {
             /**\brief:
              * The following calls seperate the vector interpolation into
              * independent scalar interpolations.
              */
             using Supports = typename pmacc::math::CT::make_Int<simDim, supp>::type;
+            using ResultType = typename T_FieldDataBox::ValueType;
 
-            typename Cursor::ValueType result;
-            PMACC_UNROLL(Cursor::ValueType::dim)
-            for(uint32_t i = 0; i < Cursor::ValueType::dim; i++)
+            ResultType result;
+            PMACC_UNROLL(ResultType::dim)
+            for(uint32_t i = 0; i < ResultType::dim; i++)
             {
-                auto fieldComponent
-                    = pmacc::cursor::make_FunctorCursor(field, pmacc::algorithm::functor::GetComponent<float_X>(i));
+                // work on a copy to shift the field for each loop round separate
+                auto shiftedField = field;
                 floatD_X particlePosShifted = particlePos;
-                ShiftCoordinateSystem<Supports>()(fieldComponent, particlePosShifted, fieldPos[i]);
+                ShiftCoordinateSystem<Supports>()(shiftedField, particlePosShifted, fieldPos[i]);
+
+                auto accessFunctor = [&](DataSpace<simDim> const& idx) constexpr
+                {
+                    return shiftedField(idx)[i];
+                };
                 result[i] = InterpolationMethod::template interpolate<begin, end>(
-                    fieldComponent,
+                    accessFunctor,
                     getShapeFunctors(particlePosShifted));
             }
 
diff --git a/include/picongpu/algorithms/ShiftCoordinateSystem.hpp b/include/picongpu/algorithms/ShiftCoordinateSystem.hpp
index 04a0fad8c4..aef47758c3 100644
--- a/include/picongpu/algorithms/ShiftCoordinateSystem.hpp
+++ b/include/picongpu/algorithms/ShiftCoordinateSystem.hpp
@@ -42,8 +42,8 @@ namespace picongpu
     template<typename T_Component, typename T_Supports>
     struct AssignToDim
     {
-        template<typename T_Type, typename T_Vector, typename T_FieldType>
-        HDINLINE void operator()(T_Type& cursor, T_Vector& pos, const T_FieldType& fieldPos)
+        template<typename T_DataBox, typename T_Vector, typename T_FieldType>
+        HDINLINE void operator()(T_DataBox& dataBox, T_Vector& pos, const T_FieldType& fieldPos)
         {
             const uint32_t dim = T_Vector::dim;
             using ValueType = typename T_Vector::type;
@@ -59,7 +59,7 @@ namespace picongpu
             const ValueType v_pos = pos[component] - fieldPos[component];
             DataSpace<dim> intShift;
             intShift[component] = GetOffsetToStaticShapeSystem<isEven>()(v_pos);
-            cursor = cursor(intShift);
+            dataBox = dataBox.shift(intShift);
             pos[component] = v_pos - ValueType(intShift[component]);
         }
     };
@@ -73,8 +73,8 @@ namespace picongpu
     {
         /** shift to new coordinate system
          *
-         * shift cursor and vector to new coordinate system
-         * @param[in,out] cursor cursor to memory
+         * shift DataBox and vector to new coordinate system
+         * @param[in,out] dataBox DataBox pointing to the particle located cell
          * @param[in,out] vector short vector with coordinates in old system
          *                        - defined for [0.0;1.0) per dimension
          * @param fieldPos vector with relative coordinates for shift ( value range [0.0;0.5] )
@@ -85,19 +85,16 @@ namespace picongpu
          * - Even Support: vector is always [0.0;1.0)
          * - Odd Support: vector is always [-0.5;0.5)
          */
-        template<typename T_Cursor, typename T_Vector, typename T_FieldType>
-        HDINLINE void operator()(T_Cursor& cursor, T_Vector& vector, const T_FieldType& fieldPos)
+        template<typename T_DataBox, typename T_Vector, typename T_FieldType>
+        HDINLINE void operator()(T_DataBox& dataBox, T_Vector& vector, const T_FieldType& fieldPos)
         {
-            /** \todo check if a static assert on
-             *  "T_Cursor::dim" == T_Vector::dim ==  T_FieldType::dim is possible
-             *  and does not waste registers */
-            const uint32_t dim = T_Vector::dim;
+            constexpr uint32_t dim = T_DataBox::Dim;
 
             using Size = boost::mpl::vector1<boost::mpl::range_c<uint32_t, 0, dim>>;
             using CombiTypes = typename AllCombinations<Size>::type;
 
             meta::ForEach<CombiTypes, AssignToDim<bmpl::_1, T_supports>> shift;
-            shift(cursor, vector, fieldPos);
+            shift(dataBox, vector, fieldPos);
         }
     };
 
diff --git a/include/picongpu/particles/Particles.kernel b/include/picongpu/particles/Particles.kernel
index 3270e804cc..4c3f017fb1 100644
--- a/include/picongpu/particles/Particles.kernel
+++ b/include/picongpu/particles/Particles.kernel
@@ -301,12 +301,10 @@ namespace picongpu
             const traits::FieldPosition<fields::CellType, FieldE> fieldPosE;
             const traits::FieldPosition<fields::CellType, FieldB> fieldPosB;
 
-            auto functorEfield = CreateInterpolationForPusher<Field2ParticleInterpolation>()(
-                eBox.shift(localCell).toCursor(),
-                fieldPosE());
-            auto functorBfield = CreateInterpolationForPusher<Field2ParticleInterpolation>()(
-                bBox.shift(localCell).toCursor(),
-                fieldPosB());
+            auto functorEfield
+                = CreateInterpolationForPusher<Field2ParticleInterpolation>()(eBox.shift(localCell), fieldPosE());
+            auto functorBfield
+                = CreateInterpolationForPusher<Field2ParticleInterpolation>()(bBox.shift(localCell), fieldPosB());
 
             /** @todo this functor should only manipulate the momentum and all changes
              *        in position and cell below need to go into a separate kernel
diff --git a/include/picongpu/particles/interpolationMemoryPolicy/ShiftToValidRange.hpp b/include/picongpu/particles/interpolationMemoryPolicy/ShiftToValidRange.hpp
index 66d39b5800..0eef70d8f9 100644
--- a/include/picongpu/particles/interpolationMemoryPolicy/ShiftToValidRange.hpp
+++ b/include/picongpu/particles/interpolationMemoryPolicy/ShiftToValidRange.hpp
@@ -35,7 +35,7 @@ namespace picongpu
                 HDINLINE T_MemoryType memory(const T_MemoryType& mem, const T_PosType& pos) const
                 {
                     const T_PosType pos_floor = math::floor(pos);
-                    return mem(precisionCast<int>(pos_floor));
+                    return mem.shift(precisionCast<int>(pos_floor));
                 }
 
                 template<typename T_PosType>
diff --git a/include/picongpu/particles/ionization/byCollision/ThomasFermi/ThomasFermi_Impl.hpp b/include/picongpu/particles/ionization/byCollision/ThomasFermi/ThomasFermi_Impl.hpp
index dfecb4e63a..495c87cb34 100644
--- a/include/picongpu/particles/ionization/byCollision/ThomasFermi/ThomasFermi_Impl.hpp
+++ b/include/picongpu/particles/ionization/byCollision/ThomasFermi/ThomasFermi_Impl.hpp
@@ -248,11 +248,11 @@ namespace picongpu
                     /* interpolation of density */
                     const picongpu::traits::FieldPosition<fields::CellType, FieldTmp> fieldPosRho;
                     ValueType_Rho densityV
-                        = Field2ParticleInterpolation()(cachedRho.shift(localCell).toCursor(), pos, fieldPosRho());
+                        = Field2ParticleInterpolation()(cachedRho.shift(localCell), pos, fieldPosRho());
                     /*                          and energy density field on the particle position */
                     const picongpu::traits::FieldPosition<fields::CellType, FieldTmp> fieldPosEne;
                     ValueType_Ene kinEnergyV
-                        = Field2ParticleInterpolation()(cachedEne.shift(localCell).toCursor(), pos, fieldPosEne());
+                        = Field2ParticleInterpolation()(cachedEne.shift(localCell), pos, fieldPosEne());
 
                     /* density in sim units */
                     float_X const density = densityV[0];
diff --git a/include/picongpu/particles/ionization/byField/ADK/ADK_Impl.hpp b/include/picongpu/particles/ionization/byField/ADK/ADK_Impl.hpp
index d23d9fc8ea..02c305d830 100644
--- a/include/picongpu/particles/ionization/byField/ADK/ADK_Impl.hpp
+++ b/include/picongpu/particles/ionization/byField/ADK/ADK_Impl.hpp
@@ -191,12 +191,10 @@ namespace picongpu
                         DataSpaceOperations<TVec::dim>::template map<TVec>(particleCellIdx));
                     /* interpolation of E- */
                     const picongpu::traits::FieldPosition<fields::CellType, FieldE> fieldPosE;
-                    ValueType_E eField
-                        = Field2ParticleInterpolation()(cachedE.shift(localCell).toCursor(), pos, fieldPosE());
+                    ValueType_E eField = Field2ParticleInterpolation()(cachedE.shift(localCell), pos, fieldPosE());
                     /*                     and B-field on the particle position */
                     const picongpu::traits::FieldPosition<fields::CellType, FieldB> fieldPosB;
-                    ValueType_B bField
-                        = Field2ParticleInterpolation()(cachedB.shift(localCell).toCursor(), pos, fieldPosB());
+                    ValueType_B bField = Field2ParticleInterpolation()(cachedB.shift(localCell), pos, fieldPosB());
 
                     IonizationAlgorithm ionizeAlgo;
                     /* determine number of new macro electrons to be created and energy used for ionization */
diff --git a/include/picongpu/particles/ionization/byField/BSI/BSI_Impl.hpp b/include/picongpu/particles/ionization/byField/BSI/BSI_Impl.hpp
index 7015248408..43d0a7cba1 100644
--- a/include/picongpu/particles/ionization/byField/BSI/BSI_Impl.hpp
+++ b/include/picongpu/particles/ionization/byField/BSI/BSI_Impl.hpp
@@ -181,8 +181,7 @@ namespace picongpu
                         DataSpaceOperations<TVec::dim>::template map<TVec>(particleCellIdx));
                     /* interpolation of E */
                     const picongpu::traits::FieldPosition<fields::CellType, FieldE> fieldPosE;
-                    ValueType_E eField
-                        = Field2ParticleInterpolation()(cachedE.shift(localCell).toCursor(), pos, fieldPosE());
+                    ValueType_E eField = Field2ParticleInterpolation()(cachedE.shift(localCell), pos, fieldPosE());
 
                     /* this is the point where actual ionization takes place */
                     IonizationAlgorithm ionizeAlgo{};
diff --git a/include/picongpu/particles/ionization/byField/Keldysh/Keldysh_Impl.hpp b/include/picongpu/particles/ionization/byField/Keldysh/Keldysh_Impl.hpp
index d5c1bf2b83..58da2ff0b3 100644
--- a/include/picongpu/particles/ionization/byField/Keldysh/Keldysh_Impl.hpp
+++ b/include/picongpu/particles/ionization/byField/Keldysh/Keldysh_Impl.hpp
@@ -191,12 +191,10 @@ namespace picongpu
                         DataSpaceOperations<TVec::dim>::template map<TVec>(particleCellIdx));
                     /* interpolation of E- */
                     const picongpu::traits::FieldPosition<fields::CellType, FieldE> fieldPosE;
-                    ValueType_E eField
-                        = Field2ParticleInterpolation()(cachedE.shift(localCell).toCursor(), pos, fieldPosE());
+                    ValueType_E eField = Field2ParticleInterpolation()(cachedE.shift(localCell), pos, fieldPosE());
                     /*                     and B-field on the particle position */
                     const picongpu::traits::FieldPosition<fields::CellType, FieldB> fieldPosB;
-                    ValueType_B bField
-                        = Field2ParticleInterpolation()(cachedB.shift(localCell).toCursor(), pos, fieldPosB());
+                    ValueType_B bField = Field2ParticleInterpolation()(cachedB.shift(localCell), pos, fieldPosB());
 
                     IonizationAlgorithm ionizeAlgo;
                     /* determine number of new macro electrons to be created and energy used for ionization */