diff --git a/RecoTracker/LSTCore/src/alpaka/Hit.h b/RecoTracker/LSTCore/src/alpaka/Hit.h
index da726ec470d02..b416a1e329b89 100644
--- a/RecoTracker/LSTCore/src/alpaka/Hit.h
+++ b/RecoTracker/LSTCore/src/alpaka/Hit.h
@@ -80,8 +80,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   }
 
   struct ModuleRangesKernel {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc1D const& acc,
                                   ModulesConst modules,
                                   HitsRanges hitsRanges,
                                   int nLowerModules) const {
@@ -100,8 +99,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct HitLoopKernel {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc1D const& acc,
                                   uint16_t Endcap,          // Integer corresponding to endcap in module subdets
                                   uint16_t TwoS,            // Integer corresponding to TwoS in moduleType
                                   unsigned int nModules,    // Number of modules
diff --git a/RecoTracker/LSTCore/src/alpaka/Kernels.h b/RecoTracker/LSTCore/src/alpaka/Kernels.h
index 40e9a0c587b3b..4c738259dfd87 100644
--- a/RecoTracker/LSTCore/src/alpaka/Kernels.h
+++ b/RecoTracker/LSTCore/src/alpaka/Kernels.h
@@ -141,8 +141,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   }
 
   struct RemoveDupQuintupletsAfterBuild {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc3D const& acc,
                                   ModulesConst modules,
                                   Quintuplets quintuplets,
                                   QuintupletsOccupancyConst quintupletsOccupancy,
@@ -188,8 +187,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct RemoveDupQuintupletsBeforeTC {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc2D const& acc,
                                   Quintuplets quintuplets,
                                   QuintupletsOccupancyConst quintupletsOccupancy,
                                   ObjectRangesConst ranges) const {
@@ -267,8 +265,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct RemoveDupPixelTripletsFromMap {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc, PixelTriplets pixelTriplets) const {
+    ALPAKA_FN_ACC void operator()(Acc2D const& acc, PixelTriplets pixelTriplets) const {
       for (unsigned int ix : cms::alpakatools::uniform_elements_y(acc, pixelTriplets.nPixelTriplets())) {
         for (unsigned int jx : cms::alpakatools::uniform_elements_x(acc, pixelTriplets.nPixelTriplets())) {
           if (ix == jx)
@@ -298,8 +295,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct RemoveDupPixelQuintupletsFromMap {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc, PixelQuintuplets pixelQuintuplets) const {
+    ALPAKA_FN_ACC void operator()(Acc2D const& acc, PixelQuintuplets pixelQuintuplets) const {
       unsigned int nPixelQuintuplets = pixelQuintuplets.nPixelQuintuplets();
       for (unsigned int ix : cms::alpakatools::uniform_elements_y(acc, nPixelQuintuplets)) {
         float score1 = __H2F(pixelQuintuplets.score()[ix]);
@@ -322,8 +318,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct CheckHitspLS {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc2D const& acc,
                                   ModulesConst modules,
                                   SegmentsOccupancyConst segmentsOccupancy,
                                   SegmentsPixel segmentsPixel,
diff --git a/RecoTracker/LSTCore/src/alpaka/MiniDoublet.h b/RecoTracker/LSTCore/src/alpaka/MiniDoublet.h
index 73dc7051fd93c..6ac9a36d1b40e 100644
--- a/RecoTracker/LSTCore/src/alpaka/MiniDoublet.h
+++ b/RecoTracker/LSTCore/src/alpaka/MiniDoublet.h
@@ -675,8 +675,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   }
 
   struct CreateMiniDoublets {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc2D const& acc,
                                   ModulesConst modules,
                                   HitsConst hits,
                                   HitsRangesConst hitsRanges,
@@ -802,12 +801,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   }
 
   struct CreateMDArrayRangesGPU {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc, ModulesConst modules, ObjectRanges ranges, const float ptCut) const {
-      // implementation is 1D with a single block
-      static_assert(std::is_same_v<TAcc, ALPAKA_ACCELERATOR_NAMESPACE::Acc1D>, "Should be Acc1D");
-      ALPAKA_ASSERT_ACC((alpaka::getWorkDiv<alpaka::Grid, alpaka::Blocks>(acc)[0] == 1));
-
+    ALPAKA_FN_ACC void operator()(Acc1D const& acc, ModulesConst modules, ObjectRanges ranges, const float ptCut) const {
       // Declare variables in shared memory and set to 0
       int& nTotalMDs = alpaka::declareSharedVar<int, __COUNTER__>(acc);
       if (cms::alpakatools::once_per_block(acc)) {
@@ -869,16 +863,11 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct AddMiniDoubletRangesToEventExplicit {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc1D const& acc,
                                   ModulesConst modules,
                                   MiniDoubletsOccupancy mdsOccupancy,
                                   ObjectRanges ranges,
                                   HitsRangesConst hitsRanges) const {
-      // implementation is 1D with a single block
-      static_assert(std::is_same_v<TAcc, ALPAKA_ACCELERATOR_NAMESPACE::Acc1D>, "Should be Acc1D");
-      ALPAKA_ASSERT_ACC((alpaka::getWorkDiv<alpaka::Grid, alpaka::Blocks>(acc)[0] == 1));
-
       for (uint16_t i : cms::alpakatools::uniform_elements(acc, modules.nLowerModules())) {
         if (mdsOccupancy.nMDs()[i] == 0 or hitsRanges.hitRanges()[i][0] == -1) {
           ranges.mdRanges()[i][0] = -1;
diff --git a/RecoTracker/LSTCore/src/alpaka/PixelQuintuplet.h b/RecoTracker/LSTCore/src/alpaka/PixelQuintuplet.h
index 0c2aa28896b7c..1923e5dfe8c3f 100644
--- a/RecoTracker/LSTCore/src/alpaka/PixelQuintuplet.h
+++ b/RecoTracker/LSTCore/src/alpaka/PixelQuintuplet.h
@@ -634,8 +634,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   }
 
   struct CreatePixelQuintupletsFromMap {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc3D const& acc,
                                   ModulesConst modules,
                                   ModulesPixelConst modulesPixel,
                                   MiniDoubletsConst mds,
diff --git a/RecoTracker/LSTCore/src/alpaka/PixelTriplet.h b/RecoTracker/LSTCore/src/alpaka/PixelTriplet.h
index ef7c4d8629718..c0e132c6ddb5d 100644
--- a/RecoTracker/LSTCore/src/alpaka/PixelTriplet.h
+++ b/RecoTracker/LSTCore/src/alpaka/PixelTriplet.h
@@ -786,8 +786,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   }
 
   struct CreatePixelTripletsFromMap {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc3D const& acc,
                                   ModulesConst modules,
                                   ModulesPixelConst modulesPixel,
                                   ObjectRangesConst ranges,
diff --git a/RecoTracker/LSTCore/src/alpaka/Quintuplet.h b/RecoTracker/LSTCore/src/alpaka/Quintuplet.h
index 345a500848d78..0ce6870a016ff 100644
--- a/RecoTracker/LSTCore/src/alpaka/Quintuplet.h
+++ b/RecoTracker/LSTCore/src/alpaka/Quintuplet.h
@@ -1642,8 +1642,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   }
 
   struct CreateQuintuplets {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc3D const& acc,
                                   ModulesConst modules,
                                   MiniDoubletsConst mds,
                                   SegmentsConst segments,
@@ -1773,16 +1772,11 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct CreateEligibleModulesListForQuintuplets {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc1D const& acc,
                                   ModulesConst modules,
                                   TripletsOccupancyConst tripletsOccupancy,
                                   ObjectRanges ranges,
                                   const float ptCut) const {
-      // implementation is 1D with a single block
-      static_assert(std::is_same_v<TAcc, ALPAKA_ACCELERATOR_NAMESPACE::Acc1D>, "Should be Acc1D");
-      ALPAKA_ASSERT_ACC((alpaka::getWorkDiv<alpaka::Grid, alpaka::Blocks>(acc)[0] == 1));
-
       // Initialize variables in shared memory and set to 0
       int& nEligibleT5Modulesx = alpaka::declareSharedVar<int, __COUNTER__>(acc);
       int& nTotalQuintupletsx = alpaka::declareSharedVar<int, __COUNTER__>(acc);
@@ -1857,15 +1851,10 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct AddQuintupletRangesToEventExplicit {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc1D const& acc,
                                   ModulesConst modules,
                                   QuintupletsOccupancyConst quintupletsOccupancy,
                                   ObjectRanges ranges) const {
-      // implementation is 1D with a single block
-      static_assert(std::is_same_v<TAcc, ALPAKA_ACCELERATOR_NAMESPACE::Acc1D>, "Should be Acc1D");
-      ALPAKA_ASSERT_ACC((alpaka::getWorkDiv<alpaka::Grid, alpaka::Blocks>(acc)[0] == 1));
-
       for (uint16_t i : cms::alpakatools::uniform_elements(acc, modules.nLowerModules())) {
         if (quintupletsOccupancy.nQuintuplets()[i] == 0 or ranges.quintupletModuleIndices()[i] == -1) {
           ranges.quintupletRanges()[i][0] = -1;
diff --git a/RecoTracker/LSTCore/src/alpaka/Segment.h b/RecoTracker/LSTCore/src/alpaka/Segment.h
index 92ed042a77d65..0e61c09bbf119 100644
--- a/RecoTracker/LSTCore/src/alpaka/Segment.h
+++ b/RecoTracker/LSTCore/src/alpaka/Segment.h
@@ -525,8 +525,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   }
 
   struct CreateSegments {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc3D const& acc,
                                   ModulesConst modules,
                                   MiniDoubletsConst mds,
                                   MiniDoubletsOccupancyConst mdsOccupancy,
@@ -620,13 +619,8 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct CreateSegmentArrayRanges {
-    template <typename TAcc>
     ALPAKA_FN_ACC void operator()(
-        TAcc const& acc, ModulesConst modules, ObjectRanges ranges, MiniDoubletsConst mds, const float ptCut) const {
-      // implementation is 1D with a single block
-      static_assert(std::is_same_v<TAcc, ALPAKA_ACCELERATOR_NAMESPACE::Acc1D>, "Should be Acc1D");
-      ALPAKA_ASSERT_ACC((alpaka::getWorkDiv<alpaka::Grid, alpaka::Blocks>(acc)[0] == 1));
-
+        Acc1D const& acc, ModulesConst modules, ObjectRanges ranges, MiniDoubletsConst mds, const float ptCut) const {
       // Initialize variables in shared memory and set to 0
       int& nTotalSegments = alpaka::declareSharedVar<int, __COUNTER__>(acc);
       if (cms::alpakatools::once_per_block(acc)) {
@@ -693,15 +687,10 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct AddSegmentRangesToEventExplicit {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc1D const& acc,
                                   ModulesConst modules,
                                   SegmentsOccupancyConst segmentsOccupancy,
                                   ObjectRanges ranges) const {
-      // implementation is 1D with a single block
-      static_assert(std::is_same_v<TAcc, ALPAKA_ACCELERATOR_NAMESPACE::Acc1D>, "Should be Acc1D");
-      ALPAKA_ASSERT_ACC((alpaka::getWorkDiv<alpaka::Grid, alpaka::Blocks>(acc)[0] == 1));
-
       for (uint16_t i : cms::alpakatools::uniform_elements(acc, modules.nLowerModules())) {
         if (segmentsOccupancy.nSegments()[i] == 0) {
           ranges.segmentRanges()[i][0] = -1;
@@ -715,8 +704,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct AddPixelSegmentToEventKernel {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc1D const& acc,
                                   ModulesConst modules,
                                   ObjectRangesConst ranges,
                                   HitsConst hits,
diff --git a/RecoTracker/LSTCore/src/alpaka/TrackCandidate.h b/RecoTracker/LSTCore/src/alpaka/TrackCandidate.h
index bea2635d341e2..8f3a6cd37d192 100644
--- a/RecoTracker/LSTCore/src/alpaka/TrackCandidate.h
+++ b/RecoTracker/LSTCore/src/alpaka/TrackCandidate.h
@@ -108,8 +108,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   }
 
   struct CrossCleanpT3 {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc2D const& acc,
                                   ModulesConst modules,
                                   ObjectRangesConst ranges,
                                   PixelTriplets pixelTriplets,
@@ -144,8 +143,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct CrossCleanT5 {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc3D const& acc,
                                   ModulesConst modules,
                                   Quintuplets quintuplets,
                                   QuintupletsOccupancyConst quintupletsOccupancy,
@@ -193,8 +191,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct CrossCleanpLS {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc2D const& acc,
                                   ModulesConst modules,
                                   ObjectRangesConst ranges,
                                   PixelTripletsConst pixelTriplets,
@@ -268,17 +265,12 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct AddpT3asTrackCandidates {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc1D const& acc,
                                   uint16_t nLowerModules,
                                   PixelTripletsConst pixelTriplets,
                                   TrackCandidates cands,
                                   SegmentsPixelConst segmentsPixel,
                                   ObjectRangesConst ranges) const {
-      // implementation is 1D with a single block
-      static_assert(std::is_same_v<TAcc, ALPAKA_ACCELERATOR_NAMESPACE::Acc1D>, "Should be Acc1D");
-      ALPAKA_ASSERT_ACC((alpaka::getWorkDiv<alpaka::Grid, alpaka::Blocks>(acc)[0] == 1));
-
       unsigned int nPixelTriplets = pixelTriplets.nPixelTriplets();
       unsigned int pLS_offset = ranges.segmentModuleIndices()[nLowerModules];
       for (unsigned int pixelTripletIndex : cms::alpakatools::uniform_elements(acc, nPixelTriplets)) {
@@ -320,8 +312,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct AddT5asTrackCandidate {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc2D const& acc,
                                   uint16_t nLowerModules,
                                   QuintupletsConst quintuplets,
                                   QuintupletsOccupancyConst quintupletsOccupancy,
@@ -371,8 +362,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct AddpLSasTrackCandidate {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc1D const& acc,
                                   uint16_t nLowerModules,
                                   TrackCandidates cands,
                                   SegmentsOccupancyConst segmentsOccupancy,
@@ -408,17 +398,12 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct AddpT5asTrackCandidate {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc1D const& acc,
                                   uint16_t nLowerModules,
                                   PixelQuintupletsConst pixelQuintuplets,
                                   TrackCandidates cands,
                                   SegmentsPixelConst segmentsPixel,
                                   ObjectRangesConst ranges) const {
-      // implementation is 1D with a single block
-      static_assert(std::is_same_v<TAcc, ALPAKA_ACCELERATOR_NAMESPACE::Acc1D>, "Should be Acc1D");
-      ALPAKA_ASSERT_ACC((alpaka::getWorkDiv<alpaka::Grid, alpaka::Blocks>(acc)[0] == 1));
-
       int nPixelQuintuplets = pixelQuintuplets.nPixelQuintuplets();
       unsigned int pLS_offset = ranges.segmentModuleIndices()[nLowerModules];
       for (int pixelQuintupletIndex : cms::alpakatools::uniform_elements(acc, nPixelQuintuplets)) {
diff --git a/RecoTracker/LSTCore/src/alpaka/Triplet.h b/RecoTracker/LSTCore/src/alpaka/Triplet.h
index ec3e6935a85c5..10446cd542c17 100644
--- a/RecoTracker/LSTCore/src/alpaka/Triplet.h
+++ b/RecoTracker/LSTCore/src/alpaka/Triplet.h
@@ -734,8 +734,7 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   }
 
   struct CreateTriplets {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc3D const& acc,
                                   ModulesConst modules,
                                   MiniDoubletsConst mds,
                                   SegmentsConst segments,
@@ -835,16 +834,11 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct CreateTripletArrayRanges {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc1D const& acc,
                                   ModulesConst modules,
                                   ObjectRanges ranges,
                                   SegmentsOccupancyConst segmentsOccupancy,
                                   const float ptCut) const {
-      // implementation is 1D with a single block
-      static_assert(std::is_same_v<TAcc, ALPAKA_ACCELERATOR_NAMESPACE::Acc1D>, "Should be Acc1D");
-      ALPAKA_ASSERT_ACC((alpaka::getWorkDiv<alpaka::Grid, alpaka::Blocks>(acc)[0] == 1));
-
       // Initialize variables in shared memory and set to 0
       int& nTotalTriplets = alpaka::declareSharedVar<int, __COUNTER__>(acc);
       if (cms::alpakatools::once_per_block(acc)) {
@@ -910,15 +904,10 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::lst {
   };
 
   struct AddTripletRangesToEventExplicit {
-    template <typename TAcc>
-    ALPAKA_FN_ACC void operator()(TAcc const& acc,
+    ALPAKA_FN_ACC void operator()(Acc1D const& acc,
                                   ModulesConst modules,
                                   TripletsOccupancyConst tripletsOccupancy,
                                   ObjectRanges ranges) const {
-      // implementation is 1D with a single block
-      static_assert(std::is_same_v<TAcc, ALPAKA_ACCELERATOR_NAMESPACE::Acc1D>, "Should be Acc1D");
-      ALPAKA_ASSERT_ACC((alpaka::getWorkDiv<alpaka::Grid, alpaka::Blocks>(acc)[0] == 1));
-
       for (uint16_t i : cms::alpakatools::uniform_elements(acc, modules.nLowerModules())) {
         if (tripletsOccupancy.nTriplets()[i] == 0) {
           ranges.tripletRanges()[i][0] = -1;