Building it cost £5bn; it took 20 years to construct, and is still to operate at full strength. Yet scientists have already turned their attention to designing a replacement for the Large Hadron Collider (LHC), the world's most powerful particle accelerator which last year revealed the existence of the Higgs boson, a subatomic entity which plays a key role in giving mass to the building blocks of the universe.

Proposals for a new machine include building a giant underground circular tunnel. This would be similar to the LHC – which is based at the Geneva HQ of Cern, the European particle physics laboratory – but would be more than 100km in diameter: four times the size of the current collider. An alternative device would hurtle particles in straight lines along a tunnel that would be more than 50km long.

In either case, the bursts of intense energy that would be released by colliding particles in these machines would help scientists probe matter to new levels. In particular, it would help them pinpoint material known as dark matter which is believed to account for most of the mass of the universe today.

According to Professor Rolf Heuer, director general of Cern, the search for the existence of dark matter provides science with one of its last great challenges. "Thanks to the LHC, scientists have demonstrated that the Standard Model – which explains the underlying structure of the cosmos's observable matter – is generally correct," Heuer told the Observer. "The discovery of the Higgs was the culmination of that work."

However, Heuer added that quarks, electrons, gluons and particles such as the Higgs account for only a small fraction of the universe's mass. Observations by astronomers of the rotation of galaxies have shown that if these bodies were made only of normal matter they would fly apart.

Another form of matter must therefore be providing an extra gravitational pull that is holding galaxies together. This dark matter is thought to be made up of Wimps – weakly interacting massive particles – that appear to account for most of the universe's mass. No one has ever observed them, however, and their detection is now the prime intellectual challenge for physics in the 21st century, Heuer added.

Heuer will be travelling to Britain this week to attend the opening of "Collider" at the Science Museum in London. The exhibition blends theatre and video with real artefacts from Cern in order to recreate the experience of visiting the LHC. Others attending the opening will be Stephen Hawking, author Ian McEwan, and Professor Peter Higgs, who predicted the existence of the Higgs boson and who won the Nobel prize for physics last month. The Observer and Guardian are media partners for the exhibition.

The LHC at Geneva is currently shut down while engineers upgrade the giant device in order to double the energies of the protons which it smashes together at colossal velocities in order to create particles that help reveal the underlying structure of the universe.

Heuer said the LHC was still on schedule to restart operations in 2015 and should begin to create a host of new particles, including some that might shed hints about the nature of dark matter. "The LHC will have another 20 years of operation," added Heuer. "I am very confident that a great many exciting discoveries will be made in that time.

"However, we have to think now what kind of machine we want to build in future in order to carry on the work of the LHC. We may get strong hints about the nature of dark matter from the LHC but it may be that we will require an even more powerful device to study them properly."

And this presents scientists with a problem – for they need results from the LHC to indicate what kind of machine should be its replacement. "However, we don't know yet if we will need a machine that collides bunches of protons or devices that collide electrons with positrons or something similar," said Heuer.

The former would probably be built as a 100km underground circular collider, a giant version of the LHC and would be able to generate beams of highly energetic protons which would then be collided with each other. Such machines produced very energetic collisions and a wide array of new particles. However, they also produce a great deal of subatomic debris, and sifting through this detritus can be difficult.

"It may be that we will need a machine that is more precise although less energetic," added Heuer. "In that case, a linear device – a long, straight tunnel – through which lighter particles like electrons are accelerated might be better. Until we get more results from the LHC we cannot be sure. However, we have to be prepared and we are looking at possible designs for both types of machine."

Heuer added that the technology that would be required to build a next-generation collider did not yet exist. In particular, current magnets – used to bend beams of particles – would not be strong enough for a new, far more powerful collider.

"However, it was the same when we began designing the LHC in the 1980s. Magnets then were not powerful enough, but we managed to design and build a new generation. I am sure we will be able to do that for the next collider as well. And that is a crucial point. These devices drive technology forward."

Cern is not the only international organisation concerned with the hunt for dark matter. At several sites in Europe and the US, detectors – stored deep underground to minimise background radiation – are straining to pinpoint the existence of dark matter Wimps. To date, they have found nothing, but researchers working there are confident they may soon succeed.

"Discovering dark matter particles is one thing," said Heuer. "It will undoubtedly be a great achievement. But a collider like the LHC or its successor should be able to do more than just detect such particles. It will be able to manufacture them so that we can study them in a controlled manner."

Crucially, Heuer added that he believed that the next-generation particle collider that is currently being studied would be so large and complex it would have to be funded by all the world's major scientific powers. The US, Europe, Japan and China would need to merge their resources to raise the tens of billions of pounds that will be needed to fund it.

Despite such global funding, he was adamant that the new machine should still be built in Europe. "Over the past few decades, Europe has provided the security and resources that have ensured particle physics has reached its current status," he said. "We have shown what Europe can do. This is the home of particle physics and it should be the home of the next great particle collider that the world constructs."