Densities achievable in ASDEX Upgrade discharges are restricted by a d
isruptive limit in the L-mode caused by an edge-power imbalance which
is linking divertor detachment, Marfe formation and the separatrix den
sity, The attainable average densities depend then on the internal par
ticle sources and the core transport and can exceed the empirical Gree
nwald density. in K-mode an upper density limit is found which represe
nts a non-disruptive H-L back transition, which is preceded by the occ
urrence of type-III ELMs. Close to the Greenwald limit this H-L transi
tion cannot be avoided at any power Bur across the separatrix and-at h
igh external neutral gas fluxes-confinement compared with ITER H-92P s
caling degrades even before the back transition. The H-mode operationa
l window is determined by local edge-barrier parameters and their grad
ients, respectively. The boundaries are represented by the L-H transit
ion-temperature threshold, the ideal ballooning edge-pressure gradient
limit, the upper temperature limit for type-III ELMs and an upper H-m
ode barrier density limitation. The cause for the last limitation is n
ot yet identified; it may be due to resistive ballooning modes or the
separatrix density limit. Despite the limited edge densities the Green
wald density could be surpassed by a factor of three with pellet refue
lling from the low magnetic-field side. Pellet injection from the high
-field side gains from the strong increase of fuelling efficiency due
to the assisting toroidal outward drift of the formed high-beta ablata
nt. Higher densities are achievable in H-mode compared with low-held s
ide injection and diminished convective losses avoid confinement degra
dation up to the Greenwald density. In gas-puffed type-I ELMy H-modes
the plasma thermal energy and the edge-pressure gradients, which are l
imited by ballooning stability, are linked via a robust temperature-pr
ofile stiffness and the flat density profiles resulting from dominant
edge refuelling at high densities. Their confinement does not improve
with increasing density (and neutral gas fluxes) and may even slightly
degrade. Therefore, the superior confinement of type-I ELMy II-modes
compared with type-Iii ELMY ones at medium densities is actually offse
t at densities close to the Greenwald density. In contrast to the temp
erature-profile resilience density profiles can be changed both by dee
p refuelling (with pellets) and intrinsic transport improvements conne
cted with density peaking (observed in CDH-modes), which offers the co
mbination of high confinement and high density operation. The possible
alliance with radiation cooling, divertor detachment and divertor com
patible type-III ELMs could solve the power exhaust problem.