50 years of Critical State


50 years ago, Charles Bean provided the superconducting community with a model efficient enough to allow computing in an understandable way the response of a superconductor to external magnetic fields and currents flowing trough the superconducting parts: the so called critical-state approach. The technical and scientific community could develop from that moment analytical and numerical approaches that could solve the electrical current distribution and the magnetization hysteretic behaviour in the most geometries and field distributions. Forces, energy concerns as losses or remanence could be solved in an equilibrium state or in a sequence of equilibrium states. Today, the critical state approach is not the only tool for designing operative superconducting systems. Other approaches tend to integrate the superconducting design in nearly standard electromagnetic CAD systems, modelling the superconducting parts and allowing also consider approaching time dependent processes.


A great effort is being made in order to provide efficient modelling tools at the level of the CAD tools developed for standard electromagnetic design as PDE solvers based on FEM or BEM in both 2D or 3D as a goal, being one of the most relevant topics to be solved for the development of an efficient Superconducting Engineering. Integrated Modelling considering Electromagnetic, thermal and mechanical concerns can be seen in a horizon.


The Workshop on HTS modelling was born in Lausane with the aim of sharing problems and solutions in the development of efficient modelling tools and was enhanced in Cambridge to offer the opportunity to continue this development effort by including industrial concepts and summary seminars. The great success of the previous workshops and the development achieved by modelling has pushed to organize a new edition of the International Workshop on HTS Modelling.


In Barcelona, ICMAB-CSIC, UPC and UAB have been honoured to host the third edition of the workshop, just in the 50th birthday of the critical state model and we will be very happy to share this event and the work done in the development of old ideas. We will have opportunity to discuss about the possible trends and rigorous ways to move towards efficient and practical concepts and tools for modelling. Superconducting Science and Engineering is waiting for it.


In this new edition of the International Workshop on HTS Modelling, to be developed from 10 to 13 April 2012 we will deal with superconducting problems and the solutions offered by the several modelling scopes, from critical state models to those based on FE method or alternatives, as well as with the pending challenges.


We will enjoy the event in a gentle city with a historical and cultural richness. We look forward to your participation.


The chairmen


International Advisory Board
  • Francesco Grilli Karlsruhe, Institut of Tecnology, Karlsruhe, (DE)
  • Enric Pardo, Institut of Electric Engineering, Bratislava (SK)
  • Archie M Campbell, University of Cambridge, Cambridge (UK)
  • Tim Coombs, University of Cambridge, Cambridge (UK)
  • Yasunori Mawatari, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba (JP)
  • Naoyuki AMEMIYA Kyoto University,Kyoto (JP)
  • Philippe Masson, University of Houston, Houston, (TX)
  • Fedor Gomory, Institut of Electric Engineering, Bratislava (SK)
  • Frederic Sirois, Ecole Polytech Montreal, Montreal, (CA)
  • Bertrand Dutois, Ecole Polytechnique Fédérale de Lausanne, Lausanne (CH)
  • Philippe Vanderbemden, Université de Liège, Liège, (BE)

Local Organizing Committee

  • Alfredo Álvarez, UNEX
  • Andreas Sumper, IREC
  • Antonio Badia, UNIZAR
  • Carles Navau, UAB
  • Elena Bartolomé, EUSS
  • Javier Mora, UPC
  • Luis García Tabarés, CIEMAT
  • Pilar Suárez, UNEX
  • Rafael Navarro, UNIZAR
  • Ricard Bosch, UPC
  • Ricardo Torres, UPC
  • Miquel Carrera (UdL)



  • Xavier Granados, ICMAB-CSIC
  • Alvar Sánchez, UAB
  • Josep López-López, UPC


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Gala Dinner will take place at 21:00, April 12th.




























Sprawled between the beaches of the Mediterranean and the hills of Montjuïc, Barcelona is a city whose personality bursts at every natural seam. The capital of Catalonia, one of Spain's 17 autonomous communities, Barcelona is also known as the country's most progressive city, always on the cutting-edge of European art, fashion and cuisine. What's more, its energy is unparalleled, with hundreds of bars, restaurants, cafes and clubs... so be prepared to party 'till dawn and hit the streets with the rest of the city's nearly 2 million inhabitants.

Cosmocaixa is the world wide known Science Museum of Barcelona. It is a privileged site in the upper side of the city.  You can enjoy its unique exhibition of experiments, its tropical forest, its architecture, its Planetarium, and a lot of activities related with Scientific knowledge. From its gardens you can get one of the most delightful views of the city landscape. An extraordinary environment for learning about the cutting edge research on numerical modelling of High Temperature Superconductors.

Busses, tramway, underground and a nice walk permit an easy access from everywhere the city. 

Isaac Newton, 26 , 08022 Barcelona

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